REESE  LIBRARY 

OF  T^ 

UNIVERSITY  OF  CALIFORNIA. 


Accessions  No.u  w^.     Cl,us  No 


-vl 


NOTES 


SCIENCE   AND  ART 


EDUCATION. 


WILLIAM  NOETLING, 

PROFESSOR   OF   PEDAGOGY,  STATE  NORMAL  SCHOOL,    BLOOMSBURG,   PA. 


NEW  YORK  AND  CHICAGO: 

E.   L.   KELLOGG  &-CO. 


Copyright,  1^95,  by 

E.  L.  KELLOGG  &  CO., 

NEW  YORK. 


PREFACE. 


I  HAVE  for  some  years  dictated  my  instructions  on  the 
science  and  art  of  teaching,  in  the  form  of  notes,  sugges- 
tions, and  hints,  to  the  junior  class  of  this  school ;  but  a 
desire  has  been  expressed  by  students  and  others  to  have 
the  work  in  a  more  convenient  shape  for  preservation  and 
use,  and  to  enable  the  many  teachers  who  do  not  have  the 
advantages  of  normal  instruction  to  avail  themselves  of  its 
helps.  In  compliance  with  this  desire  I  have  prepared  the 
notes  for  publication: ,  They  do  not,  however,  constitute 
a  methodical  or  a  complete  treatise  upon  pedagogics,  but 
only  thoughts  and  suggestions  for  prospective  teachers  and 
for  beginners  in  school-room  work. 

Every  subject  has  been  treated  with  as  much  fullness, 
as  well  as  brevity,  as  my  experience  has  shown  necessary. 
To  subjects  in  which  beginners  need  most  help  I  have 
given  more  space  than  to  others  ;  this  accounts  for  the  dis- 
proportion in  the  number  of  pages  devoted  to  different 
subjects. 

The  matter  will  be  found  in  harmony  with  the  best  in 
education  and  teaching,  and  presented,  it  is  hoped,  with  a 
sufficiency  of  explanation  to  make  it  intelligible  to  be- 
ginners. 

Repetitions  occur  here  and  there,  wherever  it  is  believed 
they  will  be  serviceable  to  those  for  whom  the  book  is  in- 
tended. 

WM.  NOETLING. 
STATE  NORMAL  SCHOOL, 

BLOOMSBURG,  PA., 
Dec.  19,  1894. 

3 


VALUABLE    BOOKS 

ON 

METHODS   OF  TEACHING. 


PARKER'S  TALKS  ON  PEDAGOGICS 
PARKER'S  TALKS  ON  TEACHING 
CALKINS'  How  TO  TEACH  PHONICS     . 
SINCLAIR'S  FIRST  YEAR  AT  SCHOOL 
SEELEY'S  GRUBE  METHOD  OF  NUMBERS 
PAYNE'S  LECTURES  ON  TEACHING    . 
HUGHES'  MISTAKES  IN  TEACHING 
DEWEY'S  How  TO  TEACH  MANNERS  ' 
JOHNSON'S  EDUCATION  BY  DOING 

ETC.,      ETC.,      ETC. 


$1.50 
1.25 

0.50 

0.75 

1. 00 
1. 00 

0.50 
0.50 
0.50 


***  Catalogue  describing  all  of  our  publications,  over  400  in  number, 
sent  free. 


E.  L  KELLOGG  &  CO.,  NEW  YORK. 


CONTENTS. 


PACK 

AUTHOR'S  PREFACE 3 

INTRODUCTORY  CONSIDERATIONS 7 

PART    I. 
THE  CARE  OF  THE  BODY '. 8 


PART   II. 

THE  MIND n 

Chapter      I.  The  Intellect n 

Chapter    II.  The  Feelings 33 

Chapterlll.  The  Will  . 38 

PART    III. 
IMPORTANT  OBSERVATIONS  AND  INFERENCES  42 

PART   IV. 

OBJECT  LESSONS 45 

(a)  Their  Design 

(b)  The  Plan  or  Method  of  a  Lesson 

PART  V. 
PENMANSHIP 46 

PART  VI. 
PRIMARY  READING 48 

5 


6  Contents. 

PART   VII. 

PAGE 

ADVANCED  READING 57 

PART  VIII. 

NOTES  AND  SUGGESTIONS  ON  TEACHING  THE  ENGLISH  LANGUAGE. 

Chapter    I.  General  Considerations 64 

Chapter  II.    I.  Oral  Language 68 

2.  Written  Language 71 

PART  IX. 
SUGGESTIONS  FOR  TEACHING  NUMBERS  87 

•PART  X. 
GEOGRAPHY. 173 

PART  XI. 
HISTORY 185 

PART   XII. 
THE  HUMAN  BODY 189 

PART  XIII. 
CIVIL  GOVERNMENT 193 

PART  XIV. 
DRAWING 194 


NOTES  ON  THE  SCIENCE   AND 
ART  OF   EDUCATION. 


INTRODUCTORY  CONSIDERATIONS. 

1.  The   science  of  education    embraces  the  principles, 
laws,  or  knowledge  in  accordance  with  which  the  education 
of  a  child  must  be  carried  on  ;  and  the  art,  the  carrying  on 
of  the  process.     In  other  words,  the  science  is  the  knowing, 
and  the  art  the  doing. 

2.  To  conduct  the  education  of  a  child  intelligently  and 
successfully,  the  teacher  must  possess  a  thorough  knowl- 
edge of  its  constitution,  physical  and  mental. 

3.  Understanding   the   physical    constitution    implies   a 
knowledge  of  its  mechanism,  the  function  each  organ  per- 
forms, and  the  relation   the  various  organs  bear  to   one 
another. 

4.  Enjoyment  is  one  of  the  most  important  elements  in 
our  existence  upon  earth  ;  and  this  depends  upon  health — 
the  health  of  the  body  and  of  the  mind.    Preserving  health, 
or  securing  it  if  not  possessed,  is  therefore  one  of  the  first 
things,  if  not  altogether  the  first,  in  the  education  of  a  child. 

7 


THE  CARE  OF  THE  BODY. 

5.  To  preserve  the  body  in  a  healthy  state,  it  must  have 
a  proper  supply,  as  fast  as  needed,  of  the  elements  that 
enter  into  its  composition  ;  it  must  be  kept  clean,  properly 
clothed,  must  have  rest  and  exercise-;  and  be  surrounded 
by  suitable  light  and  proper  conditions  of  atmosphere. 

6.  The  body  is  composed  of  a  number  of  kinds  of  mate- 
rial, and  the  quantity  of  each  necessary  at  any  time  to  pre- 
serve the  health  and  strength  of  every  organ  and  power 
depends  upon  the  kind  of  activity  in  which  the  person  is 
engaged,  or,  in  other  words,  upon  the  amount  of  activity  of 
each  organ  and  power.    For  example,  if  the  muscles  chiefly 
are  exercised,  the  material  of  which  they  are  formed  must 
be  supplied  in   sufficient  quantity  to  make  up  for   their 
waste — the  amount  destroyed  by  use  ;   if  the  bones,  the 
material  of  which  they  are  made  must  be  supplied  in  suffi- 
cient quantity  to  make  up  for  their  loss  by  use  ;  and  if  the 
brain  and  nerves,  the  kind  of  material  that  builds  them  up 
must  predominate  in  the  nourishment  taken. 

7.  The  proper  nourishment  of  the  body  does  not,  how- 
ever, alone  depend  upon  the  quantity  of  any  kind  of  food 
taken,  but  more,  perhaps,  upon  the  quality  and  upon  the 
preparation  it  has  received. 

8.  Another  important  condition  of  food  is  variety.     An 
unvaried  diet  destroys  both  appetite  and  health.     Walker, 
in  his  Physiology,  says  :  "  The  system  craves  a  varied  diet, 
and  living  for  a  length  of  time  on  even  an  abundance  of 
food,  if  it  be  unvaried  from  day  to  day,  will  generally  result 


The  Care  of  the  Body. 


in  loss  of  appetite  and  in  disease.  *  *  *  When  a  variety 
of  articles  cannot  be  obtained,  varied  methods  of  preparing 
and  cooking  the  limited  supply  should  be  resorted  to. 
'  Good  cookery  means  economy;  bad  cookery  means  waste/ 
"  On  the  other  hand,  however,  there  may  be  such  a  thing 
as  too  great  a  variety,  and  this  also  will  destroy  the  appe- 
tite." 

"  It  is  a  dictum  of  mental  as  well  as  physical  hygiene  that  it 
is  far  better  to  stint  one's  self  along  any  other  line  rather  than 
deprive  ourselves  of  food  of  needed  quality  and  quantity.  I 
say  stint,  for  it  is  not-  economy.  Poor  food  means  poor  blood 
and  not  enough  of  it,  and  this  in  turn  means  a  brain  starving 
for  oxygen.  Such  a  brain  is  always  a  weary  brain,  slow  to  re- 
spond and  erratic  in  its  activities;  and  this  fatigued,  poisoned 
brain  can  pever  sustain  mental  processes  of  high  character  or 
strict  integrity.  Therefore,  I  say,  that  in  treating  of  the  re- 
ciprocal influence  that  obtains  between  body  and  mind,  the 
question  of  diet  is  one  of  special  importance  to  those  having 
the  care  of  children,  and  should  be  discussed  at  great  length 
by  educators  in  order  that  it  may  receive  in  every  quarter  the 
attention  it  so  richly  deserves." — Krohn,  Practical  Lessons  in 
Psychology. 

9.  Exercise,  too,  at  proper  times,  and  suitable  in  kind 
and  amount,  is  a  necessity  to  health  and  comfort.     But 
exercise  of  any  part  of  the  body  tears  it  down — in  other 
words,  gradually  wears  it  out,  consumes  its  tissues  ;  and  if 
this  process  is  continued  too  long  or  faster  than  new  ones 
are  formed  to  take  the  places  of  those  that  have  been  de- 
stroyed,  pain,   in  form  of   weariness  or  fatigue — nature's 
warning — ensues,  and  is  a  sign  that  the  safety-point  has 
been  passed  and  that  rebuilding  is  necessary. 

10.  Rebuilding  of  brain  requires  more  time  than  that  of 
muscle  or  of  bone  ;  brain-workers,  therefore,  demand  more 
sleep  than  those  who  chiefly  exercise  their  muscles.     But 
sleep  should   be   sound,  unbroken.     Students,  when   per- 
mitted to  do  so,  frequently  study  at  hours  of  the  night  when 
they  should  sleep,  and  afterwards  try  to  sleep  when,  from 
exhaustion  or  worry,  they  are  unable  to  do  so.     But  wake- 

(UNIVERSITY) 

V       0,,,°'         ul. 


Science  and  Art  of  Education. 


fulness,  when  the  physical  system  needs  repairs  through 
rest,  implies  some  kind  of  functional  disorder,  and  un- 
doubtedly is  a  premonition  of  brain-exhaustion.  Dr.  J.  L. 
Corning,  an  authority  on  cerebral  diseases,  says  :  "  Derange- 
ment in  the  function  of  sleep  is  an  infallible  sign  that  the 
proper  relation  between  waste  and  repair  of  brain-tissue  no 
longer  exists;  and  that,  unless  the  undue  expenditure  of 
brain-force  be  made  to  cease,  cerebral  bankruptcy  is  im- 
pending. *  *  *  The  injury  produced  upon  the  thought 
and  emotional  centres  by  a  high  degree  of  worry,  conjoined 
with  undue  intellection,  it  is  almost  impossible  to  over- 
estimate; indeed,  a  very  large  percentage  of  cases  of  brain- 
exhaustion  is  directly  traceable  to  this  baneful  combination 
of  causes." 

11.  When  sleeplessness,  headache,  loss  of  appetite,  languor 
on  rising  in  the  morning,  and  general  debility  manifest  them- 
selves, and  drugging  begins,  the  danger-signals  are  clearly  in 
view,  and,  if  not  heeded,  a  wreck  is  sure  to  follow.  (For  a 
fuller  treatment  on  securing  and  preserving  health,  see 
Walker's  Physiology  and  Martin's  The  Human  Body.) 


THE  MIND. 


CHAPTER  I. — THE  INTELLECT. 

12.  Method  of  Studying  It.— What  mind  is  we  do  not 
know,  in  fact  cannot  know  ;  for  it  is  not  a  material  thing,  a 
thing  that  can  be  cognized  by  the  senses.     Like  electricity 
and  magnetism,  it  can  be  studied  only  through  its  manifesta- 
tions or  effects.     This  method  of  learning  is  that  of  in- 
ference, inferring  causes  from   their  effects — learning  the 
promptings  of  the  mind  by  the  appearances  and  muscular 
activities  that  follow  them,  and  that  seem  to  be  their  effects 
or  that  we  infer  to  be  their  effects.     Mental  states  and 
activities  must  therefore  be  studied  inductively.  Generaliza- 
tions must  be  cautiously  made,  and  no  conclusion  hastily 
drawn.      Facts,  sufficient  in   number,  must   be  observed, 
noted,  and  classified,  before  a  valid  conclusion  can  safely 
be  reached.     Nor  will  one  person's  facts  serve  any  purpose 
for  those  of  another  ;  each  must  make  his  own  observations, 
classifications,  and  draw  his  own  conclusions.    This  is  what 
each  must  learn  to  do  in  order  to  become  a  student  of 
mental  phenomena.     Neither  the  teacher  nor  any  one  else 
can  do  it  for  him  ;  all  the  help  that  any  one  can  give  him  is 
to  show  him  how  to  study  himself  and  others,  and  how  to 
test  his  conclusion. 

13.  The  Body  the  Servant  of  the  Mind.— The  mind 
manifests  itself  through  the  body,  performs  all  its  observable 


Science  and  Art  of  Education. 


or  visible  work  through  it  ;  and  one  of  the  objects  of  educa- 
tion is  the  training  of  the  body  to  become  the  obedient  and 
skilful  servant  of  the  mind. 

REMARK. — Under  no  circumstances  must  the  mind  become 
the  mere  servant  of  the  body,  or  the  body  be  allowed  complete 
control  of  the  mind. 

14.  Forms  of  the  Material  World  and  How  Cognized. 

— The  material  world  presents  itself  to  us  in  six  different 
forms:  i.  Colors  and  figures  ;  2.  Sounds  ;  3.  Heat  and  cold  ;  4. 
Hardness  and  softness,  smoothness  and  roughness;  5.  Tastes; 
6.  Smells.  And  the  organs  through  which  these  forms  are 
cognized  are  the  senses,  the  feelers — seeing,  hearing,  touch- 
ing, tasting,  and  smelling.  It  is,  however,  the  mind  that 
sees,  hears,  touches,  tastes,  and  smells,  and  not  the  organs 
which  it  uses  to  do  so. 

15.  When  an  object  affects  a  sense-organ,  the  nerves  con- 
nected with  the  organ  convey  the  impression  to  the  mind  ; 
in  other  words,  make  the  mind  conscious  of  it.     If  the 
object  is  of  sufficient  interest  or  importance  at  the  time,  the 
mind  observes  it  and  takes,  so  to  speak,  an  impression  or 
image  of  it.     This  impression  is  termed  a  percept. 

REMARK. — A  percept  remains  before  the  mind,  or  in  con- 
sciousness, only  as  long  as  the  object  which  gives  rise  to  it 
affects  the  sense-organ. 

16.  Attention. — In  order  that  the  mind  may  be  in  the 
most  favorable  state  for  the  reception  of  impressions,  certain 
conditions  are  necessary.     One  of  the  most  important  of 
these  is  attention,  or  the  concentration  of  the  mind  upon 
the  object  examined  or  subject  studied. 

17.  For  educational  purposes,  attention  may  be  divided 
into  two  kinds,  apparent  and  real ;  the  former  being  only 
the  appearance  of  attention,  the  latter  the  reality. 

18.  Real  attention  may  be  either  attracted  or  directed, 
and  divided  or  undivided. 


The  Intellect.  13 


REMARK. — Attracted  attention  is  also  called  non-voluntary 
(without  an  effort  of  the  will),  and  directed,  voluntary  (by  an 
effort  of  the  will). 

19.  Apparent  and  divided  attention,  having  no  value  in 
education,  need  no  further  consideration  here. 

20.  Attracted  attention  is  that  which  is  given  from  interest 
or  novelty  in  the  subject  examined  or  studied,  and  depends 
upon  the  teacher's  ability  to  make  the  subject  of  instruction 
interesting  or  attractive. 

REMARK.— Attracted  attention  is  the  only  kind  that  can  be 
expected  from  children. 

21.  Directed,  or  voluntary,  attention  is  that  which  comes 
from  an  effort  of  the  person  giving  it.     This  kind  can  be 
expected  from  persons  of  sufficient  age  and  judgment  to 
appreciate  the  value  of  subjects  of  study,  but  not  from 
children.      Voluntary  attention  must,  however,  ultimately 
change  to  non-voluntary.    If  it  fails  to  do  this,  the  teaching 
is  defective — a  failure. 

22.  Attention  cannot  be  given  equally  well  under  all  cir- 
cumstances.      Its   most    successful    efforts   depend   upon 
certain  conditions  ;  the  most  important  of  which  are  :  (i) 
good  health,  (2)  good  light,  (3)  pure  air,  (4)  proper  temper- 
ature,   (5)    comfortable   seats,   (6)   absence  of   distracting 
objects,  (7)  proper  position,  and  (8)  close  classification. 

23.  Conditions  of  attention,  however  important,  do  not 
imply  attention  ;  they  imply  simply  that  everything  neces- 
sary, so  far  as  the  pupils  and  their  surroundings  are  con- 
cerned, has  been  supplied.     The  next  thing  to  do  is  to 
secure  attention,  and  this  not  all  teachers  can  do  with  equal 
success.     As  a  requisite,  to  begin  with,  the  teacher  must 
have  the  confidence  of  his  pupils.   He  should  be  :  (i)  master 
of  the  subjects  he  teaches;  (2)  unhampered  by  the  use  of  a 
text-book  during   recitation;  (3)   cheerful;   (4)  interested; 
(5)  in  earnest.    He  should  begin  where  the  children's  knowl- 
edge ends  ;  and  should  excite  curiosity. 


1 4  Science  and  Art  of  Education. 

REMARK. — The  teacher  should  not  abruptly  pass  from  one 
subject  to  another,  but  should  by  gradual  steps  lead  his  pupils 
to  it.  Inattention  is  frequently  caused  by  abrupt  transitions. 

24.  Attention   must  not   only  be  secured,  but  must  be 
continued  or  held.     The  following  suggestions,  if  carried 
out  in  the  proper  spirit,  not  merely  in  a  mechanical  manner 
will   aid  the  teacher  in  keeping  the  attention  of  his  pupils  : 
i.  Do  not  attempt   to  teach  anything  that  is  beyond  the 
ability  of  the  pupils  ;  2.  Keep  curiosity  aroused  ;  3.  Let  the 
age  of  the  pupils  determine  the  length  of  the  lesson  ;  4.  Let 
the  advancement  determine  the  subject  and  the  lesson  ; 
5.   In  teaching  children,  sense-wholes  should  be  taught  be- 
fore their  parts  ;  6.  Go  from  the  known  to  its  related  un- 
known ;  7.  As  a  general  rule,  tell  nothing  to  pupils  which 
they  can  find  out  themselves  or  be  led  to  find  out ;  8.  Vary 
your  mode  of  instruction,  your  mode  of  presenting  subjects  ; 
9.  As  far  as  possible,  give  every  pupil  a  share  in  the  reci- 
tation ;    10.  Use  illustrations   and   apparatus;   n.  Do  not 
teach  longer  than  you  have  the  attention  of  your  pupils  ; 
12.  Utilize  the  instincts — activity,  curiosity,  imitation,  etc. 

REMARK  ON  CONDITION  10  OF  THE  FOREGOING. — If  you 
have  apparatus,  teach  with  it.  Requiring  pupils  to  prepare 
lessons  from  imperfect  descriptions  or  poorly-made  illustrations 
or  pictures,  when  a  school  has  the  apparatus  with  which  the 
subject  may  be  studied,  is  inexcusable. 

REMARK  ON  SECURING  AND  HOLDING  ATTENTION.— To 
secure  and  to  hold  attention,  something  new  must  be  presented, 
or  the  mode  of  presentation  must  be  new.  No  one  can  give 
continued  attention  to  that  which  yields  nothing. 

25.  Like  the  other  powers  of  the  mind,  attention  may 
be  cultivated.     The  following  are  some  of  the  means  that 
may  be  used  for  this  purpose  :  i.  Read  or  relate  something 
of  interest  and  value  to  the  pupils,  to  be  reproduced  by 
them ;  2.  Require  them  to  reproduce  from  memory  a  con- 
versation, lecture,  address  ;  3.  Require  the  reproduction  of 
a  problem  read  to  them  or  by  them  ;  4.  Require  the  repro- 
duction of  a  paragraph,  article,  or  selection  read  by  them. 


The  Intellect.  15 


REMARK. — Special  periods  for  the  purpose  of  cultivating  the 
power  of  attention  are  not  to  be  recommended  ;  for  the  same 
ends  may  generally  be  attained  in  the  regular  classes  with  the 
daily  work. 

26.  Attention  Depending  upon  Pupils*  State  of  Mind. 
— Besides  the  foregoing  conditions  of  attention,  there  are 
others  which,  on  account   of  their  relation  to  successful 
school-work,  are  of  sufficient  importance  to  merit  separate 
consideration,     i.  The  pupils  may  be  tired  ;  2.  Their  minds 
may  be  occupied  with  something  to  them  of  more  interest 
than  that  which  the  teacher  is  endeavoring  to  introduce  ;  3. 
They  may  be  in  a  so-called  neutral  or  indifferent  state  ;  4. 
They  may  be  in  a  state  of  expectancy — waiting,  with  inter- 
est, for  the  lesson  to  be  commenced. 

In  the  first  case,  they  should  either  be  excused  from  fur- 
ther work,  or  given  some  such  exercises  as  the  making  of 
forms  of  different  kinds  of  material  ;  work  in  which  they 
can  be  interested  and  which  will  not  tire  them. 

The  second  state  may  be  one  of  antagonism  or  opposi- 
tion, one  in  which  they  refuse  to  take  part  or  interest  in 
the  subject  which  the  teacher  desires  to  introduce.  In  this 
case  the  only  remedy  is  to  prepare  the  way,  step  by  step, 
by  the  introduction  of  something  which  shall  cause  them  to 
forget  their  former  thoughts  and  thus  prepare  them  for  the 
introduction  of  the  lesson  for  the  period. 

The  third  condition  needs  the  same  kind  of  preparatory 
treatment  as  the  second,  the  only  difference  being  that,  as 
a  general  thing,  it  requires  less  effort  on  the  part  of  the 
teacher. 

In  the  fourth  condition  the  pupils  are  eagerly  waiting  for 
the  lesson  to  begin,  and  consequently  need  no  preparation 
for  it. 

27.  Perception — Observation — Reflection. — As    already 
stated,  the  impression  which  an  object  makes  upon  the 
mind  through  the  senses  is  called  a  percept  ;  in  other  words, 


1 6  Science  and  Art  of  Education. 

a  percept  is  a  mental  construction  of  an  external  object — a 
construction  in  the  mind  by  the  mind  itself. 

A  percept  is  a  product,  and  the  operation  or  act  that 
gives  rise  to  it  is  perception. 

Percepts  are  of  two  kinds,  original  and  acquired. 

REMARK  i. — Some  psychologists  apply  the  term  perception 
to  a  complete  mental  picture  of  an  external  object,  and  percept 
to  a  single  element  of  it  obtained  through  one  of  the  senses. 

REMARK  2. — Perceptive  knowledge,  or  that  obtained  from 
the  direct  or  immediate  apprehension  of  an  object,  is  also  called 
presentative  knowledge,  and  its  revival  or  representation  from 
memory,  representative  knowledge. 

28.  Our  knowledge   begins  with  experience  ;  it  depends, 
consequently,  upon  the  completeness  and  clearness  of  our 
percepts  ;  and  the  quality  of  our  percepts  depends  upon 
observation — upon  attention  to  all  the  particulars  or  char- 
acteristics of  an  object.     Careful  observation  therefore  lies 
at  the  foundation  of  education. 

29.  Not  only  can  the  mind  observe  the  outer,  the  world 
of  matter,  but  it  can  also  turn  itself  in  upon  itself,  so  to 
speak,  and  scan  its  own  states  and  activities.     This  process 
— observing  what  the  mind  itself  is  doing — is  called  intro- 
spection, reflection  ;  sometimes,  internal  perception. 

30.  Memory. — Memory    (figuratively   speaking)   is    the 
mind's  treasure-house,  the  power  of  preserving  and  recalling 
the  facts  of  consciousness.     When  attention  is  withdrawn 
from  an  object,  its  percept  passes  from  consciousness  to 
the  memory. 

31.  For  the  convenience  of  study,  memory  may  be  con- 
sidered under  two  distinct  heads,  retention  and  recollection. 
Retention  is  the  mind's  power  of  holding  or  preserving  the 
facts  of  consciousness,  and  recollection  that  of  bringing 
them  forth  when  they  are  wanted. 

REMARK. — James  Mark  Baldwin,  in  his  Elements  of  Psychol- 
ogy, says : 
"  In  considering  the  entire  mental  function  which  we  call 


The  Intellect.  17 


memory,  we  find  that  it  involves  several  factors  or  stages, 
which  are  sometimes  treated  as  distinct  operations,  but  may 
properly  be  considered,  as  we  find  them,  together.  Together 
they  constitute  a  chain  of  events  whereby  the  mental  life  of  the 
past  is  retained  and  utilized  in  the  present.  First,  there  is  the 
permanent  possibility  of  the  revival  of  a  past  experience  when 
its  first  circumstances  are  repeated;  this  is  called  Retention. 
Next,  there  is  the  actual  return  of  the  image  to  consciousness  : 
Reproduction.  Third,  this  image  is  known  as  having  already 
been  presented  in  our  past  experience :  Recognition.  And 
finally  there  is,  in  most  cases,  an  immediate  reference  to  the 
exact  past  time  of  its  first  experience  :  Localization  in  time. 
These,  taken  together,  constitute  a  finished  act  of  memory. 
Accordingly,  memory  may  be  defined  as  a  mental  revival  of  a 
conscious  experience" 

32.  As  before  remarked,  when  an  object  of  perception 
no  longer  affects  or  stimulates  a  sense-organ,  no  percept  of 
it  is  in  consciousness  ;  recollection  therefore  does  not  bring 
percepts  before  the  mind,  but  transcripts,  mental  represen- 
tations, images,  ideas,  or  concepts  of  them. 

REMARK  i.— The  term  concept  is  preferable  to  that  of  idea 
for  recalled  mental  pictures,  because  idea  is  used  in  so  many 
senses  as  to  lead  to  confusion  in  the  minds  of  students  of  men- 
tal phenomena.  Trench  says :  "  The  word  idea  is,  perhaps,  the 
worst  case  in  the  English  language.  One  person,  for  example, 
has  an  idea  that  the  train  has  started,  another  had  no  idea  that 
the  dinner  was  so  bad." 

REMARK  2. — Conception  is  a  constructing  process,  and  its 
products  are  concepts. 

REMARK  3. — All  forms  in  which  past  experiences  may  be  re- 
called and  brought  before  the  mind  will  in  these  pages  be  con- 
sidered as  representations  or  mental  pictures,  and  all  mental 
pictures,  except  percepts,  as  concepts. 

33.  The   mind's  power  to  retain  facts  depends   greatly 
upon  the  state  or  condition  in  which  it  is  when  it  receives 
them.     Among  the  most  important  conditions  of  retention 
are  the  following  :  i.  Healthy  and  fresh  state  of  body  and 
mind  ;  2.  Undivided  attention  ;    3.  Thorough,    clear,  and 
distinct  comprehension  ;  4.  Lively  and  sincere  interest  ;  5. 
Determination,  or   force  of  will  ;  6.  Repetition  ;    7.  Suffi- 
cient time  for  the  impression  to  be  made. 


1 8  Science  and  Art  of  Education. 

34  An  examination  of  the  foregoing  conditions  of  reten- 
tion reveals  the  fact  that  retention  is  not  an  active  power 
of  the  mind,  and  that  it  is  cultivated  only  through  the  ac- 
tivity of  the  other  powers  ;  its  highest  degree  of  success 
depends,  therefore,  upon  the  perfection  of  the  activity  of  the 
other  powers. 

35.  Mental  images  play  an  important  part  in  remember- 
ing. Kay,  in  his  book  on  the  memory  (page  208,  etc.),  says  : 

"  The  subject  of  mental  images  is  one  that  has  hitherto  re- 
ceived but  little  attention,  and  yet  it  is  one  of  the  deepest  in- 
terest, and  calculated  to  throw  light  upon  many  obscure  mental 
phenomena.  Whenever  a  sensation  or  an  idea  is  presented  to 
the  mind,  a  mental  image  or  conception  of  it  must  be  formed 
in  order  to  its  being  perceived  or  understood.  In  proportion 
to  the  clearness  and  distinctness  of  the  image  will  be  the  under- 
standing of  it  by  the  mind,  and  the  hold  taken  of  it  by  the 
memory. 

"  As  there  are  different  kinds  of  sensations  and  different 
classes  of  ideas,  there  exists  a  like  variety  among  mental 
images  ;  and  some  minds  excel  in  some,  others  in  other.  Thus, 
some  may  excel  in  the  formation  of  visual  images,  others  of 
auditory  ones.  The  former  will  remember  best  those  things 
that  are  presented  to  the  eye,  and  of  which  they  can  form 
visual  images ;  the  latter,  such  as  are  addressed  to  the  ear,  and 
form  auditory  ones.  The  former  will  take  in  and  remember 
what  they  read,  the  latter  what  they  hear  ;  the  one  will  learn  a 
language  most  easily  by  the  eye,  from  books  ;  the  other  by  the 
ear,  from  conversation.  Some,  in  listening  to  a  discourse, 
image  every  word  they  hear  as  it  appears  to  the  eye ;  while 
others,  with  the  auditory  faculty  largely  developed,  will  image 
what  they  read  as  if  it  were  addressed  to  the  ear.  Others, 
again,  in  reading  or  in  listening  to  a  discourse,  will  attend  only 
to  the  sense  or  meaning,  and  form  sense-images.  These  can 
give  the  substance  of  what  they  have  read  or  heard  with  great 
accuracy,  though  they  may  not  perhaps  be  able  to  recall  any  of 
the  words.  In  each  case  it  is  of  importance  to  ascertain  in 
what  direction  the  image-forming  power  of  the  mind  chiefly 
lies. 

"  Further,  not  only  are  there  images  of  the  eye  and  ear,  and 
of  the  other  senses,  but  there  are  also  images  of  muscular 
movements,  as  of  the  tongue  and  hand.  Some  may  not  re- 
member much  of  what  they  see  or  hear,  but  remember  readily 
what  they  say  or  do.  Hence  some  children  learn  best  by  re- 
peating aloud,  others  by  writing  down  what  they  wish  to  remem- 


The  Intellect.  19 


her.  Most  persons  have  probably  observed,  in  writing  a  word 
in  regard  to  the  spelling  of  which  they  are  sometimes  in  doubt, 
that  if  they  write  it  at  once,  without  thinking  about  it,  they 
usually  spell  it  correctly;  but  if  they  doubt  and  hesitate  and 
think,  they  become  uncertain,  and  most  probably  spell  It  wrong. 
The  reason  is  that  the  mental  image  which  directs  the  hand  is, 
in  this  instance,  a  surer  guide  than  that  furnished  by  the  intel- 
lect. In  such  cases  the  more  the  mind  is  engaged  in  thought 
the  less  able  is  it  to  listen  to  those  inner  promptings  of  our  na- 
ture— the  muscular  images  of  past  movements,  on  which  so 
much  that  is  finest  and  most  delicate  in  our  action  depends. 

"  But  not  only  are  there  in  the  mind  mental  images  of  sensi- 
ble objects,  and  of  muscular  movements,  of  what  we  feel  and 
what  we  do,  but  every  thought,  however  abstract  or  apparently 
disconnected  from  sensible  objects,  has  its  image  in  the  mind. 
We  can  only  conceive  an  abstraction  by  having  an  image  of  it. 
The  abstract  idea  of  a  triangle,  which  is  not  any  particular  tri- 
angle, but  represents  the  properties  common  to  all  triangles, 
has  as  much  its  image  in  the  mind  as  any  individual  triangle 
that  may  have  been  before  it.  Further,  we  mast  regard  each 
abstract  idea  as  having  a  physical  state  corresponding  to  it ; 
and  hence  we  can  localize  abstract  ideas  and  recall  the  occa- 
sions when  they  were  present." 

36.  Not  only  must  facts  be  retained  in  the  mind  for 
future  use,  but  they  must  be  recalled  when  wanted.    Minds 
differ  much  in  their  recalling  power  ;  some  readily  recall 
one  kind  of  facts,  others  another  kind  ;  but,  in  either  case, 
the  ease  with  which  they  can  be  brought  forth  depends 
upon  the  manner  in  which  they  were  stored  away  in  the 
memory.     If  they  are  associated,  or  presented  to  the  mind, 
in  a  systematic,  related  manner,  they  will  be  returned  in 
the  same  manner,  every  link  in  the  chain  of  ideas  suggest- 
ing its  neighbor. 

37.  Concepts  or  ideas  may  for  educational  purposes  be 
associated  in  four  ways  :   i.   By  contiguity;  2.  By  similarity; 
3.  By  contrast;   4.  By  cause  and  effect.     Contiguity  means 
adjoining,  contact  ;  similarity,  likeness,  resemblance  ;  con- 
trast, dissimilarity  ;  cause,  that  which  produces  a  change, 
an  effect ;  and  effect,  that  which  has  been  brought  about 
or  produced  by  a  cause, 


Science  and  Art  of  Education. 


REMARK. — Other  modes  of  association  besides  the  foregoing" 
are  sometimes  given  by  writers  on  psychology,  but  as  they  are 
of  no  service  to  teachers,  they  are  here  omitted. 

38.  The  underlying  principle  of  contiguous  association 
is  that  concepts  or  experiences  which  occur  together  or  in 
immediate  succession  afterwards  tend  to  revive  one  another 
Observation,  too,  seems  to  teach  that  the  mind  integrates 
or  "  completes  any  process  upon  which  it  enters,  if  it  has 
performed  the  same  process  before." 

39.  Contiguity  may  be   in  time  or  in  place.     One  thing 
suggests  another  that  appeared  before  the  mind  with  it  or 
immediately  before  or  after  it.     Things  that  were  before 
the  mind  either  at  the  same  time  or  in  successive  time,  or 
that  were  before  it  together  in  space  (place),  are  revived 
together  or  have  a  tendency  to  reappear  together. 

REMARK. — A  number  of  dissimilar  objects  may  be  placed  in 
a  fixed  order  and  remembered  or  recalled  in  that  order,  by  as- 
sociating them  in  the  mind  invariably  in  the  same  order. 

40.  An   object  or  concept  will  bring  before  the  mind 
others  that  bear  a  resemblance  or  an  analogy  to  it.     When 
a  relation  of  some  kind  can  be  discovered  among  objects 
or  concepts,  and  this  relation  is  made  the  basis  of  a  sys- 
tematic arrangement  of  the  objects  or  concepts,  so  that  any 
one  in  the  series,  in  consequence  of  the  relation,  will  sug- 
gest the  next,  the  recalling  process  is  much  easier  than 
when  the  association  is  arbitrary,  mechanical,  without  re- 
lation. 

41.  By  the  association  of  similars  we  are  enabled  to  form 
classes  of  objects  or  concepts,  on  account  of  their  resem- 
blance in  form,  material,  or  quality,  and  to  recall  them. 
By  their  resemblances,  also,  we  trace  the  relations  of  words 
and  thus  discover  their  meanings.     The  study  of  languages 
is  greatly  shortened  by  the  association  of  similars. 

42.  For  the  purpose  of  firmly  fixing  anything  in  the  mind 
and  readily  recalling  it  when  it  is  wanted,  association  by 


The  Intellect. 


contrast  is  more  serviceable  than  association  by  resemblance 
or  analogy.  Tate,  in  his  Philosophy  of  Education,  says  : 
"  Associations  of  resemblance  are  rarely  so  vivid  as  those 
of  contrast ;  and  hence  it  follows  that  scenes  or  events 
which  are  in  contrast  with  each  other  are  more  likely  to*  be 
remembered  than  those  which  have  a  resemblance.  Con- 
trast, like  light  and  shadow,  makes  the  objects  more  promi- 
nent." 

REMARK.— Only  such  things  as  have  some  points  of  similarity 
can  be  contrasted.  Those  which  cannot  be  compared  cannot 
properly  be  contrasted. 

43.  Landon,  in  his  School  Management,  says  :  "  The 
natural  relationship  which  links  ideas  by  means  of  cause 
and  effect  renders  them  eminently  suggestive  of  one 
another  ;  and  where  the  connection  exists,  to  fix  it  clearly 
in  the  mind  is  one  of  the  most  powerful  means  of  associa- 
tion at  our  disposal.  It  is  especially  valuable  in  lessons 
from  the  physical  or  natural  sciences  ;  and  should  be  much 
more  generally  employed  in  the  teaching  of  such  subjects 
as  history  than  it  appears  to  be." 

Tate,  the  author  above  quoted,  says  :  "  The  minds  of 
children  are  so  constituted  that  they  most  readily  remember 
effects  in  connection  with  their  causes  ;  for  example,  they 
readily  associate  the  light  of  day  with  the  presence  of  the 
sun  ;  storms  with  winds  and  clouds  ;  the  heat  of  summer 
with  the  long  days  of  sunshine  ;  the  improvement  of  the 
mind  with  application  to  study  ;  misery  with  crime,  and 
happiness  with  virtue  ;  and  so  on.  Associations  of  this 
kind  are  most  interesting  and  instructive  ;  one  idea  be- 
comes the  nucleus  of  a  whole  series,  and  idea  becomes 
so  linked  with  idea  that  we  are  enabled  to  form  a  con- 
tinuous chain  of  them.  Thus  we  readily  remember  the 
following  chain  of  associations  :  Rain  falls  from  the  clouds  ; 
the  clouds  are  chiefly  formed  by  winds  and  mountains  ;  the 
cold  on  the  tops  of  the  mountains  condenses  the  moisture 


52  Science  and  Art  of  Education. 

in  the  air,  and  thus  clouds  are  formed  ;  the  cold  on  the 
tops  of  the  mountains  is  caused  by  the  thinness  of  the  air, 
etc. ;  thin  air  is  colder  than  dense  air,  because  it  has  greater 
capacity  for  heat,  and  so  on." 

44.  From  the  foregoing  statements  concerning  the  link- 
ing of  concepts  it  will  readily  be  observed  that  there  are 
really  but  two  forms,  or  modes,  of  association,  arbitrary  or 
mechanical,  and  philosophical  or  logical.     Association  by 
contiguity  is  arbitrary  or  mechanical,  and  the  association 
of  concepts  by  such  a  relationship  that  one  calls  into  con- 
sciousness another  bearing  a  resemblance  of  some  kind  to 
it,  or  belonging  to  the  same  logical  connection,  is  properly 
termed  philosophical  or  logical. 

45.  Association  by  contiguity,  of  necessity,  has  its  place 
in  the  acquisition  of  knowledge;  but  philosophical  or  logical 
relationships  are  more  valuable  in  the  development  of  the 
mind,  because   they  call   into  activity  the   higher  mental 
powers.     No   philosophical   or   logical   bond   can   be  dis- 
covered without  thought. 

REMARK.— Children  and  the  illiterate  depend  chiefly  upon 
mechanical  associations ;  older  people,  and  especially  the  edu- 
cated, use  philosophical  or  logical  relationships. 

46.  There  is  only  one  mode  of  acquiring  facility  in  the 
suggesting,  or  recalling,  process,  and  that  is  intelligent,  per- 
sistent practice. 

47.  The  following  are  some  of  the  subjects  that  may  be 
taught  by  resemblance  and  contrast. 

A.  RESEMBLANCE. — a.  Geography.  —  North  and  South 
America  ;  South  America  and  Africa  ;  California  and  Spain 
or  France  ;  Italy  and  India  ;  Australia  and  Cuba  ;  £Jorth 
America  and  Europe  ;  Pennsylvania  and  Missouri  or  West 
Virginia  ;  New  York  and  Boston  or  Chicago  ;  Baltimore 
and  Philadelphia  ;  Richmond  and  Albany  ;  Atlantic  Ocean 
and  Pacific  Ocean  ;  products  of  East  Indies  and  West 


The  Intellect.  23 


Indies  ;  climate  and  products  of  southern  U.  S.  and  those 
of  India  ;  etc. 

b.  History. — Settlement  of  Massachusetts  and  of  Virginia, 
of  New  York  and  of  Massachusetts,  of  Pennsylvania  and  of 
Maryland,  of  Ohio  and  of  Connecticut,  of  California  and  of 
Kansas,  of  New  Jersey  and  of  Georgia ;  Washington's  and 
Jefferson's  administrations,  Washington's  and  Lincoln's  ; 
Columbus  and  Captain  Cook,  Lincoln  and  Garfield,  Grant 
and  Napoleon,  Bacon  and  Newton,  Pestalozzi  and  Horace 
Mann,  Bryant  and  Longfellow,  Daniel  Webster  and  Jrhn 
C.  Calhoun,  Horace  Greeley  and  John  Bright  ;  etc. 

B.  CONTRAST. — a.   Geography. — The  Old  World  and  the 
New  ;  the  two  hemispheres  (eastern  and  western);  London 
and  New  York  ;  Spain  and  Italy  ;  coast  of  Europe  and  of 
North  America  ;  eastern  coast  of  North  America  and  west- 
ern coast  of  same  ;  valley  of  the  Mississippi  and  that  of  the 
St.    Lawrence  ;    North   and    South   America ;    Africa  and 
South  America  ;  Philadelphia  and  Chicago  ;  etc. 

b.  History. — Settlement  of  Jamestown  and  of  Massachu- 
setts Bay  Colony  ;  colonists  of  Virginia  and  of  Massachu- 
setts ;  Dutch  of  New  York  and  Quakers  of  New  Jersey  and 
Pennsylvania ;    colonists   of    Maryland    and   of   Virginia ; 
Washington  and  Jefferson  ;  Clay  and  Webster  ;  etc. 

c.  Physical  Geography. — Surface  ot  Pennsylvania  and  of 
New  York  ;  climate  of  Pennsylvania  and  of  New  York  or 
Massachusetts  ;    products  of  Pennsylvania  and  of  Massa- 
chusetts, Maine,  or  Virginia  ;  climate  and  productions  of 
North   America   and   of    South    America ;    valley   of   the 
Danube  and  of  the  Mississippi  ;  climate  and  productions  of 
Russia  and  of   France,  of   Ireland   and   of   Australia,   of 
Arabia  and  of  India,  of  Siberia  and  of  British  America,  of 
Southern  Africa  and  of  the  southern  part  of  South  America, 
of  North  Temperate  and  South  Temperate  Zone  ;  etc. 

C.  MISCELLANEOUS. — Octagon    and   circle  ;    degrees   of 
hardness  and  softness  ;  resemblances  of  color  ;  light  and 


Science  and  Art  of  Education. 


heat  ;  cylinder,  cone,  and  sphere  ;  forms  of  letters  of  the 
alphabet  ;  spelling  of  words  of  similar  forms  and  sounds; 
etc. 

48.  The  learning  of  words   depends   upon   association. 
The  child  associates  the  name  of  a  word  with  the  form  of 
the  word,  and  either  one  of  them  suggests  the  other.     So 
also  in  acquiring  knowledge  are  the  names  of  things  asso- 
ciated with  the  things  themselves,  and  thus  remembered 
and  recalled. 

REMARK.  —  The  work  of  the  primary  teacher  consists  largely 
in  helping  the  children  to  form  permanent  associations. 

49.  Repetition  and  reviews  constitute  the  main  reliance 
for  forming  lasting  associations  ;  but  the  repetitions  and 
reviews  must  not  be  allowed  to  become  monotonous.  Pleas- 
urable emotions,  or  interest,  can  be  excited  and  kept  up  in 
no  other  way  than  by  variety  and  novelty. 

50.  If  memory  is  found  weak  in  any  particular  direction,  — 
in  recalling  names,  dates,  etc.,  for  example,  —  and  any  one's 
duties  demand  much  work  of  this  kind,  the  only  remedy  is 
daily  exercises  of  the  kind  required.     It  is  wonderful  to 
what  an  extent  the  memory  can  be  trained  in  any  special 
direction  by  persistent  efforts. 

51.  Sully  says  :  "  Committing  anything  to  memory  is  a 
severe  demand  on  the  brain-energies,  and  should,  so  far  as 
possible,  be  relegated  to  the  hours  of  greatest  vigor  and 
freshness.     The   morning  is  the   right   time   for   learning. 
In  addition  to  selecting  the  best  time,  every  resource  should 
be  used  to  make  the  subject  as  interesting  as  possible." 

REMARK.  —  A  ready  memory  is  undoubtedly  an  invaluable 
possession,  yet  it  needs  to  be  carefully  kept  within  its  legitimate 
bounds  ;  it  should  not  be  permitted  to  supplant  any  of  the  other 
powers  —  perception,  imagination,  judgment,  etc. 

52.  Imagination.  —  Imagination  is  the  power  which  forms 
or  constructs  mental  images.     It  is  divided  into  constructive, 
reconstructive,  and  productive  invention. 


The  Intellect.  2$ 


53.  Construction   may  take  place  from   observation   or 
from  description — from  what  we  ourselves  observe  or  from 
what  we  learn  from  others.     Perceiving  is  a  constructing 
process  ;  it  is  forming  images  in  the  mind  ;  and  though  not 
generally  called  imagination,  it  deserves  as  much  that  name 
as  any  other  picturing   process  performed   by   the   same 
power. 

54.  In  the  study  of  all  branches  of  knowledge  in  which, 
in  the  absence  of  the  objects  or  phenomena,  mental  pictures 
are  required,  the  imagination  constructs  and  paints  them. 
In  the  study  of  geography  and  history  the  use  of  the  con- 
structive imagination  is  indispensable. 

55.  Reconstruction  takes  place  in  recollection  or  from 
memory  ;  it  is  rebuilding  that  which  at  some  previous  time 
had  been  built  or  formed  ;  it  is  constructing  according  to  a 
former  pattern  or  model. 

56.  Reconstruction  is  employed  in  all  recitation.     The 
pupil  reconstructs  his  former  constructions,  and  the  teacher 
and  the  class  observe  whether  they  are  correct  or  reasonable. 

REMARK. — The  criticisms  made  by  the  teacher  and  the  pupils 
should  enable  the  one  who  recites  to  correct  and  complete  his 
constructions.  Simply  pointing  out  errors,  without  indicating 
how  they  may  be  corrected,  has  some  value  ;  but  pointing  them 
out  in  such  a  way  as  shall  enable  the  student  to  see  them  and 
correct  them  is  the  proper  way  to  make  the  corrections.  Criti- 
isms  should  always  be  helps,  not  hindrances. 

57.  Production,  or  invention,  has  reference  to  original 
combinations  or  constructions.     The  ability  to  make  these 
cannot  be  directly  taught  ;  it  can  only  be  encouraged,  not 
learned  ;  it  can  only  be  acquired  by  those  who  have  the 
talents  and  the  patience — by  continued  study  and  practice. 
One  who  succeeds  in  the  highest  forms  of  original  construc- 
tion is  said  to  be  a  genius. 

58.  The  teacher  should  not  only  allow  his  pupils  the 
exercise  of  originality,  but  should  encourage  it  whenever  it 
is  practicable  to  do  so.    Throwing  them  as  much  as  possible 


2 6  Science  and  Art  of  Education. 

upon  their  own  resources  is  one  of  the  best  ways  of  doing 
this. 

59.  Currie,  in   his  Principles  and  Practice  of  Common- 
School  Education,  says  : 

"  Observation  is  limited  by  very  narrow  boundaries  of  time 
and  space ;  to  whatever  extent  we  pass  these,  it  must  be  on  the 
wings  of  imagination.  Accordingly,  descriptions  of  natural 
scenery  and  scenes  from  life,  real  or  ideal,  are  the  field  in  which 
this  mode  of  intelligence  must  be  exercised  ;  and  both  are  very 
rich  in  materials. 

"  When  the  pupil  has  observed  the  elements  of  the  landscape 
at  home,  he  is  required  to  carry  these  abroad  and,  by  modifica- 
tion, interchange,  and  amplification,  to  construct  another  land- 
scape there;  the  hill,  rivulet,  meadow,  and  wood  of  his  own 
native  district  become  the  snow-clad  peak  or  volcano,  the 
mighty  river,  the  far-spreading  desert  or  cultivated  plain,  the 
trackless  forest,  of  other  lands  ;  from  the  summer's  heat  and 
winter's  ice,  whose  effects  he  observes  at  home,  he  passes  to  the 
heat  of  tropical,  and  the  cold  of  arctic,  regions,  with  the  lux- 
uriant vegetation  of  the  one  and  the  stunted  growth  of  the 
other;  the  plants  and  animals  of  his  own  country,  with  their 
interesting  habits,  serve  as  a  standard  by  which  he  may  estimate 
their  representatives  in  other  countries;  and  the  notions  of  the 
adaptations  of  labor,  and  the  modes  of  life,  which  he  forms 
from  what  he  sees  around  him,  are  drawn  upon  to  construct 
pictures  of  industry  and  the  habits  of  other  races  of  his  fellow- 
men.  Then  it  is  largely  by  the  imagination  that  a  knowledge 
of  life  is  gained,  whether  of  individuals  or  of  communities.  The 
life  of  home  or  school,  and  the  life  of  society  so  far  as  the  child 
sees  it,  are  limited  in  their  incidents ;  yet  the  teacher  hesitates 
not  to  tell  or  read  the  story  of  human  life,  in  its  spheres  and 
with  its  diversified  enjoyments,  in  the  belief  that  the  pupil's 
experience,  narrow  as  it  may  be,  will  enable  him  to  realize  the 
emotions  portrayed,  and  gather  up  the  lessons  suggested. 
Biography  and  history  are  the  natural  sources  of  supply  for 
materials  of  this  sort;  narratives  of  adventure  by  sea  or  land  ; 
descriptions  of  manners  and  customs ;  incidents  in  the  life  of 
men  or  societies  which  embody  the  virtuous  emotions  of  our 
nature.  Ideal  life  may  come  in  to  increase  the  store  of  materials ; 
it  is  equally  rich  in  instruction  with  the  life  recorded  in  history 
itself." 

60.  The  happiness  of  childhood  depends  almost  wholly 
upon  the  use  of  the  imagination.     The  plays  of  children  are 
nearly  all  imitations  of  the  real  work  of  older  people,  and 


The  Intellect.  27 


serve  as  a  preparation  for  the  later  actual  duties  of  life. 
Thus  they  make  dolls,  dress  them,  feed  them,  put  them  to 
bed  and  rock  them  to  sleep  ;  they  cook,  bake,  set  tables, 
wash  dishes,  clean  house,  make  parties,  receive  callers, 
build  dams,  mills,  houses,  railroads,  forts  ;  ride  horses,  keep 
store  ;  act  soldiers,  doctors,  preachers,  teachers,  etc. 

REMARK. — The  statement  is  sometimes  made  that  the  imagi- 
nation is  more  active  in  childhood  than  it  is  at  any  later  period 
of  life,  but  such  an  opinion  rests  upon  superficial  observation 
or  investigation.  The  imagination  is  not  stronger,  or  more 
active,  in  early  life  than  it  is  at  a  later  period ;  on  the  contrary, 
it  is  weaker,  but  its  activities  are  more  noticeable,  because  nearly 
all  of  them  are,  of  necessity,  imitations  of  the  actual  work  of 
grown  people. 

61.  The  use  of  the  imagination  is  required  in  every  calling 
in  life.      Nothing  can  be  done  intelligently  and  skilfully 
without  a  mental  picture  as  a  pattern.  The  mechanic,  the 
dressmaker,  the  baker,  the  cook,  the  farmer,  the  doctor, 
the  lawyer,  the  orator,  the  preacher,  all  must  use  it  to  meet 
with  success  in  their  vocations. 

62.  To  feel  with  a  person  and  for  a  person,  it  is  necessary 
to  imagine  ourselves  in  his  place.     The  chief  reason  why 
some    persons   seem   to   be    unsympathetic    is   that   their 
imaginative  powers  are  sluggish   or  dull;  they  cannot  place 
themselves  in  the  position   of  those  who  are  in  sorrow  or 
distress. 

63.  The  imagination  is  the  faculty  which  constructs  forms 
of  beauty  ;  it  is  therefore  one  of  the  powers  that  give  culture 
to  taste  and  refinement. 

64.  James  Freeman  Clarke  says  :   "  No  man  can  be  wholly 
unhappy  who  is  accustomed  to  look  for  beauty  in  nature 
and  in  human  life.     His  is  a  joy  which  never  wearies. 

"  All  mere  drudgery  tends  to  stupefy  the  imagination  ; 
and  all  work  is  drudgery  which  is  done  mechanically,  with 
the  hand  and  not  with  the  mind;  when  we  are  not  trying  to 
do  our  work  as  well  as  possible,  but  only  as  well  as  necessary. 


Science  and  Art  of  Education. 


Such  work  stupefies  the  ideal  faculty,  quenches  the  sense  of 
beauty.  '  No  matter  how  lowly  the  labor  may  be,  if  a  man 
performs  it  as  well  as  he  can,  he  is  an  artist.'  But  when  a 
man  tries  to  shirk  his  work,  when  he  does  it  in  a  slovenly 
manner  or  way,  not  as  well  as  he  might,  then  he  becomes  a 
drudge,  even  though  his  work  be  that  of  a  poet  or  a  sculp- 
tor. He  ceases  to  exercise  his  ideal  faculty,  and  stupefies 
it.  Then  the  sense  of  beauty  dies  out  of  his  mind. 

"  If  men  are  taught  to  look  for  beauty  in  all  that  they 
see,  to  embody  it  in  all  that  they  do,  the  imagination  will 
be  both  active  and  healthy.  Life  will  then  be  neither  a 
drudge  nor  a  dream,  but  will  become  full  of  God's  life  and 
love,  and  we  will  be  brought  into  the  love  of  that  divine 
beauty  which  is  above  all,  through  all,  and  in  us  all." 

65.  Explanation  of  Terms  —  i.  Analysis  consists  in 
separating  a  complex  whole,  whether  material  or  mental, 
into  its  elements  —  the  parts  of  which  it  is  composed.  2. 
Synthesis  consists  in  forming  a  whole  of  its  parts.  3.  Ab- 
straction is  mentally  withdrawing  certain  characteristics  or 
qualities  from  objects.  It  may  also  be  regarded  as  the 
withdrawing  of  the  mind  from  all  the  other  properties  of 
objects  except  those  under  special  consideration.  4.  Gen- 
eralizing is  finding  the  general  or  common  characteristics 
in  a  number  of  objects  or  concepts.  5.  Classification  is 
grouping  similars  into  classes,  and  embraces  generalization. 
6.  Comparison  is  simultaneously  giving  attention  to  several 
objects  to  discover  their  agreements  or  differences.  7. 
General  concept  is  the  term  applied  to  a  class,  or  to  a  group 
of  all  the  common  properties  of  the  objects  that  compose 
the  class.  A  general  concept,  therefore,  cannot  be  imag- 
ined, it  can  only  be  thought.  8.  To  apprehend  is  to  seize, 
to  take  possession  of  ;  to  comprehend  is  to  understand.  9. 
A  thing  is  known  when  it  is  assigned  to  its  proper  class. 
10.  Apperception  is  the  appropriation  of  the  new  by  the 


The  Intellect.  29 


old  ;  it  is  an  organizing  process,  n.  Elaboration  is  an- 
other name  for  thinking. 

66.  Judging. — When  the  mind  compares  two  objects  or 
concepts  directly  with  each  other  to  determine  their  rela- 
tion, the  process  is  termed  judging,  and  the  result  is  a 
judgment.  The  objects  compared  may  both  be  physical 
(material)  or  mental,  or  one  may  be  physical  and  the  other 
mental ;  that  is,  we  may  compare  one  object  (physical  or 
mental)  or  act  with  another,  or  we  may  compare  it  with  our 
concept  of  it  or  of  what  it  should  be.  The  concept  or 
image  is  then  taken  as  the  standard,  or  measure,  of  the 
comparison.  Determining  whether  a  thing  is  sour,  sweet,  or 
bitter  ;  hard  or  soft ;  cold  or  warm  ;  black  or  white  ;  weak 
or  strong  ;  coarse  or  fine  ;  suitable  or  unsuitable  ;  good  or 
bad  ;  right  or  wrong,  are  all  acts  of  judgment. 

"  We  judge  whenever  we  affirm  or  deny  one  thing  of  an- 
other. Everything  we  know,  or  think  we  know,  involves 
an  element  of  judgment,  and,  when  it  becomes  distinct 
knowledge,  can  be  explicitly  set  forth  in  a  proposition. 

"An  expressed  judgment  is  a  proposition." — Sully. 

67.  Without  the  use  of  judgment,  no  advance  step  can 
be  taken  in  the  acquisition  of  knowledge.     Judgment  is 
among  the  earliest  powers  exercised  by  children  ;  every 
act  of  discrimination   requires   it — is   an    act   of   judging. 
Ideation  employs  it  in  completing  its  images. 

REMARK  i. — Thinking  is  a  general  term  applied  to  discover- 
ing relations ;  and  its  three  successive  stages  are  conception, 
judging,  and  reasoning. 

REMARK  2. — The  several  intellectual  processes  through  which 
the  material  of  knowledge  passes  from  the  concrete  to  the  com- 
plete general  concept  are  also  usually  given  as  three  :  i.  Com- 
parison ;  2.  Abstraction  ;  3.  Generalization. 

REMARK  3. — The  last  step  in  the  conceiving  process  is  that 
of  denomination,  giving  a  name  to  the  concept. 

68.  Judgments  may  be  explicit  or  implicit ;  that  is,  we 
may  judge  consciously  or  unconsciously. 


30  '       Science  and  Art  of  Education. 

69.  Reasoning. — Not  all  objects  or  concepts  can  be  di- 
rectly compared  with  each  other.     Whenever  direct  com- 
parison is  impossible,  a  third  object  or  concept  must  be 
found  with  which  each  of  the  others  can  be  compared  and 
their  relation  determined. 

REMARK. — Frequently  more  than  one  intermediate  term  of 
comparison  is  necessary  to  determine  the  relation  of  the  two 
objects  or  concepts  under  consideration. 

70.  When  the  relation  of  two  objects  or  concepts  is  de- 
termined through  on    or  more  intermediate  ones,  the  pro- 
cess is  called  reasoning.     Examples  of  reasoning  :   i.  Given 
the  cost  of  4  Ibs.  of  butter,  to  find  the  cost  of  3  Ibs.     Here 
the  intermediate  term,  or  number,  is  i  Ib.     2.  To  find  the 
number  of  men  that  can  build  80  rods  of  wall  in  16  days, 
if  12  men  can  build  50  rods  in  15   days.     Here  there  are 
two  intermediate  terms,  rods  and  days ;  and  the  terms  of 
comparison  are  one  rod  and  one  day.     3.  A  house  and  lot 
costing  $6750  were  sold  at  a  gain  of  12^  per  cent.  ;  how 
much  was  received  for  them  ?     Here  the  term  of  compari- 
son is  i  per  cent.     4.  On  butter  sold  at  40  c.  the  gain  was 
25  per  cent.  ;  what  was  the  cost  ?     Here  the  term  of  com- 
parison is  i  per  cent.     5.  Stealing  is  a  violation  of  law ;  a 
violation  of  law  is  a  crime  ;  therefore  stealing  is   a  crime. 
Here  the  intermediate  term  is  a  violation  of  law.     6.  Per- 
sons who  tell  falsehoods  are  not  believed  when  they  tell 
the  truth  ;  Alias  tells  falsehoods  ;  therefore  he  is  not  be- 
lieved when    he    tells  the    truth.     Here  the  inteumediate 
term  is  falsehoods. 

71.  Kinds  of  Reasoning — There  are  two  kinds  or  modes 
of  reasoning,  the   inductive    and  the   deductive.     When  a 
general  truth  is  inferred  or  discovered  from  the  examination 
and  comparison  of  a  number  of  individual  facts  the  process 
is  called  induction  ;  and  when  a  particular  truth  is  found 
through  a  general  truth  it  is  called  deduction.     The  appli- 
cation of  general  principles  to  cases  that  come  under  them 


The  Intellect.  3 1 


or  are  included  in  them  is  also  deduction.  When  the  child 
finds  that  a  hot  stove,  a  gas-flame,  a  hot  coal,  etc.,  burn  its 
fingers,  and  that  fire  is  the  general  cause  of  the  heat,  it 
comes  to  the  conclusion  that  fire  burns  ;  and  it  reaches 
this  conclusion  inductively.  Afterwards  when  the  child 
keeps  its  fingers  from  hot  objects,  it  does  so  because  it  rea- 
sons deductively  that  all  hot  objects  burn. 

72.  All  the  known  laws  that  govern  the  material  universe 
have  been  learned  by  induction.      The  naturalist  cannot 
make  nature's  laws  ;  he  can  only  discover  them. 

73.  Leading  pupils  to  discover  their  own  rules,  principles, 
and  definitions,  from  the  examination  of  a  number  of  spe- 
cial cases,  is  inductive  teaching.     The  deductive  method  is 
the  reverse  of  the   inductive  ;  by  this  method  pupils  are 
taught  to  apply  rules,  principles,  and  definitions. 

REMARK. — The  inductive  is  the  method  of  acquiring  knowl- 
edge ;  the  deductive,  of  using  it. 

74.  The  Quantity  of  General  Concepts — Concepts,  be- 
ing aggregates,  or  syntheses,  of  attributes  or  properties,  are 
said  to  have  quantity.     By  the  intensive  quantity  of  a  con- 
cept is  meant  the  sum  of  the  qualities  which  constitute  it 
and  distinguish  it  from  other  classes  of  concepts  ;  and  by 
the  extensive  quantity  is  meant  the  sum  of  the  concepts 
that  may  be  classed  under  it.     Thus,  a  quadruped  is  an 
animal  having  four  feet ;  four  feet  constitute  the  intensive 
quantity  ;  and  the  number  of  animals  having  four  feet,  the 
extensive  quantity  of  the  term  quadruped. 

75.  Formal  Reasoning. — Every  logical  form  of  argument 
(syllogism)    or    reasoning   consists    of    three    propositions, 
judgments,   or  statements,   called,  respectively,  the   major 
premise,  the  minor  premise,  and  the  conclusion.     The  sub- 
ject and  the  predicate  of  a  proposition  are  called  its  terms  ; 
the  major  term  being  that  of  widest  scope,  or  extent,  in  the 
major  premise  ;  the  minor,  that  of  least  extent  in  the  minor 
premise  ;  and  the  middle,  that  found  in  both  the   others, 


3  2  Science  'and  Art  of  Education. 

and  through  which  they  are  compared.  The  middle  term 
includes  the  minor  and  is  itself  included  in  the  major.  Ex- 
ample :  A  is  B  (is  included  in  B).  C  is  A  (is  included  in 
A)  ;  therefore  C  is  B  (is  included  in  B).  Or,  taking  a 
concrete  example  :  Man  is  mortal  ;  Smith  is  a  man  ;  there- 
fore Smith  is  mortal. 

76.  Systematization. — Arranging  concepts  or  classes  of 
objects  according  to  some  order  or  plan  is  called  systema- 
tizing.   Arranging  the  classes  or  the  grades  of  a  school,  the 
goods  in  a  store,  our  daily  work,  etc.,  are  examples  of  sys- 
tematizing. 

77.  Intuition. — Intuition   means   immediate    beholding. 
We  can  immediately  behold  facts  of  matter  and  of  mind, 
and  we  can  immediately  behold,  or  cognize,  necessary  and 
universal   principles.     The  senses  behold  facts  of  matter 
and  of  mind  ;  and  therefore  give  us  empirical  intuitions,  or 
percepts ;    the   Reason    beholds    necessary   and   universal 
principles,  and  gives  us  rational  intuitions. 

78.  Of  the  correctness  of  no  other  knowledge  can  we 
have  less  doubt  than  of  our  rational  intuitions.     For  exam- 
ple, we  can  for  a  certainty  know  that  things  which  are  equal 
to  the  same  thing  are  equal  to  each  other ;  that  the  whole 
of  anything  is  greater  than  any  one  of  its  parts  ;  that  every 
effect  must  have  a  cause  ;  that  no  object  can  exist  without 
time  or  space. 

REMARK. — A  principle  or  truth  is  necessary  when  we  cannot 
think  its  contrary;  it  is  universal  when  it  is  believed  and  true 
throughout  the  universe — when  it  has  no  exceptions. 

79.  Sources  of  Knowledge — As  has  already  been  shown, 
the  mind  has  three  sources  of  knowledge,  perception  (em- 
pirical  intuition),  thought  (logical   conclusions),  and  the 
Reason  (rational  intuitions) 

REMARK. — Perception,  memory,  imagination,  comparison, 
abstraction,  generalization,  conception,  judging,  reasoning,  sys- 
tematizing and  rational  intuition,  belong  to  the  intellect,  the 
knowing  power, 


CHAPTER  II.— THE  FEELINGS. 

80.  Numerous  divisions  of  the  feelings  have  been  made 
by  psychologists  ;    the  following,  from  Dr.  A.    Schuyler's 
Empirical  and  Rational  Psychology,  are  among  the  simplest, 
i.  Physical:  sensations,  instincts,  and  appetites.     2.  Vital: 
feelings  of  rest,   as  fatigue,  of  vigor  or  languor,   and  of 
health    or    sickness.     3.  Psychical  :    emotions,    affections, 
and  desires. 

REMARK. — Sensations   are   feelings.    A  sense  is  an   organ 
through  which  we  feel ;  hence  the  senses  are  feelers. 

81.  Our  feelings  may  also  broadly  be  divided  into  pleasures 
and  pains,  or  into  physical  feelings   and  mental  feelings. 
Physical  feelings  come  from  affections  o(  the  physical  or- 
ganism, and  mental  feelings  from  cognitions  and  thoughts. 

Mental  feelings,  in   general,  without  regard   to  the  usual 
subdivisions,  will  alone  be  considered  here. 

82.  Mental    feelings   are   both   causes   and   effects  ;    as 
causes  they  move  the  mind  to  action,  and  as  effects  (as  be- 
fore stated)  they  result  from  cognitions  and  thoughts. 

83.  Our  pleasures  and  our  pains,  our  joys  and  our  sor- 
rows, depend   upon   our  feelings  ;  or,  perhaps  better,  are 
themselves  states  of  feeling.     Whatever  produces  pleasant 
or  agreeable  feelings  is  done  with  comparative  ease  ;  and 
whatever  causes  painful  or  unpleasant  feelings  is  wearisome 
and  exhaustive.     Whatever  excites  the  feelings  pleasurably 
is    said   to   be   interesting ;    and   whatever   is    interesting 
strengthens  us  and  hence    aids  us  in  the  performance  of 
duty.     Discouragements,  worry,  or  whatever  else  depresses 
the   feelings,  reduces  strength  and  is  a  hindrance  to  the 
performance   of   work,     Anticipation  or  hope   of   success 

33 


34  Science-  and  Art  of  Education. 

excites  pleasurable  feelings  and  consequently  lightens  labor. 
Expectant  enjoyment  as  the  fruit  of  success  strengthens  us 
and  enables  us  to  work  with  ease. 

84.  With  children,  the  time  that  intervenes  between  the 
performance  of  duty  and  its  resultant  enjoyment  must  be 
short  ;  their   experiences  are  too  limited   to  expect  much 
enjoyment   from   that  which  is  far   off   and,  to    them,  of 
doubtful  realization. 

85.  That  which  affords  immediate  enjoyment  is  its  own 
stimulus    to   interest  and  exertion  ;    but  that  which  gives 
only  anticipated,  distant  realization  of  success  and  enjoy- 
ment needs  to  be  invested  with  novelty  and  interest  to  ex- 
cite curiosity — a  desire  to  know — as  a  condition  to  lively 
attention  and  exertion. 

86.  The   motives   that  produce  pleasurable  emotions  in 
some  natures  do  not  do  so  in  others.     The  love  of  praise 
urges  some  to  action  ;  hope  of  success,  others.     A  student 
will  study  hard,  day  in  and  day  out,  early  and  late,  to  at- 
tain the  end  he  has  in  view — prosperity  or  eminence.     A 
man  will  perform  disagreeable  as  well  as  severe  physical 
labor  if  it  will  minister  to  his  ultimate  comfort  or  enjoy- 
ment.    It  is  evident,  therefore,  that  our  feelings  play   an 
important  part  in  the  performance  of  all  kinds  of  work, — 
especially  in  that  of  education — and  that  the  motives  which 
excite  them  and  urge  the  student  to  action  should  be  care- 
fully studied  by  every  one  who  desires  to  become  an  intel- 
ligent and   a  successful   teacher.     Garvey,  in  his  Human 
Culture,  says  :  "  To  interest  pupils  in  their  studies  is  the 
great  secret  of  success  in  teaching  ;  but  the  interest  of  the 
pupils  is  best  awakened  by  exciting  their  curiosity,  by  hold- 
ing out  to  them,  in  a  pleasant  manner,  whatever  of  strange, 
new,  and  wonderful  the  proposed  study  contains  to  reward 
their    perseverance    and     attention.  *  *  *    The    self-sus- 
taining power  of  pleasurable  feeling  ought  to  be  a  grand 
lever  in  the  hancls  of  the  educator.     If  we  once  make  the 


The  Feelings.  35 


subject  of  study  a  source  of  pleasure,  we  may  safely  leave 
the  mastery  of  it  to  the  spontaneous  energy  of  the  pupil's 
mind.  *  *  *  By  exciting  the  emotions  we  excite  the  inner 
forces  of  the  mind,  which  cause  it  to  expand  and  unfold  its 
faculties  jijst  as  the  influence  of  the  seasons  excites  the 
dormant  forces  of  the  plant." 

REMARK.— Excitement,  as  here  used,  does  not  mean  passion, 
but  such  interest  or  pleasurable  feeling  as  shall  carry  the  stu- 
dent through  his  work  with  comparative  ease,  such  as  shall 
arm  him  with  strength  and  urge  him  onward  to  the  reward  of 
his  labor. 

87.  Character. — What   a  man   really  is  constitutes   his 
character  ;    what    others   think   of    him,    his    reputation. 
Character  depends  largely  upon  the    feelings  ;    and  since 
character  is  the  man — makes  him  either  worthy  or  unworthy 
of  the  confidence  and  respect  of  his  fellow-men — the  moral 
feelings  cannot  be  overlooked  in  a  course  of  instruction. 

88.  The  feelings  cannot  be  educated  ;  they  are  not  think- 
ing powers  ;  they  can  only  be  trained,  and  they  must  be  so 
trained  that  right  conduct,  right  and  worthy  motives,  shall 
afford  pleasure  ;  and  wrong  and  unworthy  motives  and  con- 
duct, displeasure  and  pain. 

89.  The  character  of   the  teacher  has  much  to  do  with 
the  moulding  of  that  of  his  pupils.     He  must  be  consistent ; 
he  must  himself  be  and  do  what  he  would  have  his  pupils 
be  and  do.     He  must  not  only  hold  up  for  their  admiration 
that  which  is  noble  and  good,  but  must  exemplify  it  in  his 
own  daily  life.     He  must  show  not  only  displeasure,  but 
positive  abhorrence,  of  that  which  is  ignoble,  wrong,  mean, 
or  debasing.     Young  people,  especially  children,  are  imita- 
tive beings,  and  both  consciously  and  unconsciously  acquire 
the  habits  of  those  with  whom  they  are  frequently  associ- 
ated.    They  are  in  the  presence  of  the  teacher  five  to  six 
hours  a  day  during  not  fewer  than  six  months  of  the  year, 
and,  too,  during  the  most  pliable  period  of  their  lives  ;  that 
his  influence  must   be  the  main   factor   in   shaping   their 


36  Science  and  Art  of  Education. 

thoughts  and  habits  must  therefore  be  evident  to  all  who 
properly  consider  the  matter.  Hence  his  character  should 
constitute  one  of  the  principal  elements  of  his  qualification. 

90.  Good  conduct  comes  from  good  thoughts,  and  good 
thoughts  come  from  associations  and  surroundings  that  in- 
spire them  or  prompt  them.     The  mind  is  ever  active  ;  it 
must  have  something  to  act  upon.     Those  who  have  the 
charge  of  children  must  provide  this  material.     If  they  fail 
to  do  so,  the  children  will  make  their  own  selections  ;  and, 
owing  to  their  inexperience — their  inability  to  judge  cor- 
rectly as  to  what  is  best  for  them — and  the  natural  tenden- 
cies to  prefer  present  and  temporary  enjoyment,  to  future 
permanent  good,  they  will,  with  the  rarest  exceptions,  choose 
that  which  will  in  the  end  prove  harmful — destructive  of 
success  and  happiness. 

91.  Beautiful   surroundings,  such   as   well-arranged  and 
well-kept    school-grounds,   neat    and   clean    school-rooms, 
tastefully  decorated  walls,  are  important  factors  in  the  cul- 
tivation of  good  taste  and  right  feelings.     Nor  must   the 
teacher's  own  appearance  be  left  out  of  the  consideration. 
As  has  already  been  stated,  but  will  bear  repetition,  chil- 
dren are  imitative  creatures,  and  both  consciously  and  un- 
consciously adopt  many  of  the   habits  and  traits  of  those 
who    are    their  daily   associates.     The   teacher's    influence 
may  therefore  justly  be  considered  even  greater  than  that 
of  the  parents  ;    for,  besides  being  the   instructor  of  the 
children,  during  their  school  days  he  is  continually  in  their 
presence,  and  this  causes  them  to  be  impressed  more  or 
less  firmly  not  only  with  his  appearance,  but  even  with  his 
modes  of  speech  and  action. 

92.  Children   should   be   trained   to   conscientiousness  ; 
they  should  be  led  to  take  pleasure  in  that  which  is  right 
and  good,  and  to  hate  that  which  is  wrong  and  bad.     Lan- 
don,  in  his  School  Management,  says  :  "Although  the  germ 
of  the  conscience  is  born  within  us,  it  depends  almost  en- 


The  Feelings.  37 


tirely  upon  the  kind  and  extent  of  the  moral,  religious,  and 
intellectual  training  we  undergo  as  to  what  strength  and 
correctness  of  action  it  shall  attain.  We  should  therefore 
lose  no  opportunity  of  associating  emotions  of  pleasure  and 
satisfaction  with  right  doing,  of  enlightening  the  children 
as  much  as  possible  as  to  the  nature  of  various  actions,  of 
strengthening  the  judgment  by  suitable  exercises,  and  of 
ennobling  the  sense  of  duty.  The  cultivation  of  the  con- 
science so  that  it  may  be  a  sure  guide  to  the  children,  and 
that  they  may  readily  obey  its  dictates,  should  engage  the 
teacher's  attention  throughout  the  period  of  school  life. 
This  training  is  for  the  most  part  indirect,  but  it  is  none 
the  less  important  and  should  be  none  the  less  sure." 

93.  The  feelings  cannot  decide  as  to  what  is  right  or  what 
is  wrong  ;  decisions  belong  to  the  knowing  powers.     The 
feelings  can  only  prompt  the  will  to  choose  and  to  act  in 
accordance  with   the  decisions  of  the  intellect.     The  feel- 
ings are  moved  by  the  intellect,  and  can  be  changed  alone 
by  it.     Good  thoughts  produce  good  feelings  ;  bad  thoughts, 
bad  feelings  ;  sad  thoughts,  sad  feelings  ;  pleasant  thoughts, 
pleasant  feelings  ;  angry  thoughts,  angry  feelings.     Angry 
feelings  can  be  changed  to  good  or  pleasant  feelings  by 
changing  the  thoughts  that  give  rise  to  them  to  others  of  a 
good  or  pleasing  nature. 

94.  We  are   responsible   for  our  thoughts  and  feelings. 
The  fact  that  we  can  change  them  proves  it. 

95.  Strong    feeling,    excitement,    or     passion    prevents 
sound,  sober  thought.     It  is  impossible  to  reason  with  an 
angry  person.    If  we  desire  to  reason  with  him,  we  must  tell 
him  an  amusing  anecdote  or  something  else  that  will  change 
the  subject  of  his  thoughts.     The  same  (as  before  stated) 
applies  to  pupils  in  a  school.     If  any  of  them  are  angry  or 
sulky,  they   cannot   study.     The   remedy  is   a   change   of 
thought,  by  means  of  an  anecdote,  an  interesting  talk  or 
conversation,  an  illustration,  or  an  experiment. 

REMARK. — Conscience  includes  knowing  and  feeling. 


CHAPTER  III— THE  WILL. 

96.  The  only  power  of  the  mind  whose  operations  remain 
to  be  considered  is  the  will.     This  is  the  power  that  directs, 
chooses,  and  acts;  it  is  the  executive  power  of  the  mind. 
It  directs  the  intellect — gives  it  its  work,  sets  it  in  motion, 
and  waits  for  its  conclusions.     If  the  thing  considered  by 
the  intellect  is  capable  of  ministering  to  our  gratification  or 
well-being,  a  desire  or  longing  for  it  follows.     It  remains, 
then,  for  the  will  to  be  governed  by  this  desire,  or  to  refuse 
to  do  so,  in  view  of  other  considerations. 

REMARK. — One  of  the  distinguishing  characteristics  of  will 
is  a  conscious  effort  to  attain  a  known  end. 

97.  The  manifestations  of  will  may  be  classed  under  two 
heads,  untrained  and  trained;  in  other  words,  brute  and 
rational.     An  untrained  will  is  one  that  is  governed  by  im- 
pulse or  passion.     A  person  under  the  influence  of  such  a 
will  disregards  the  light  of  judgment  and  reason,  and  is 
therefore  said  to  act  contrary  to  reason,  to  be  unreasonable, 
stubborn,  obstinate,  headstrong,  ungovernable.     This  state 
of  will  is  that  of  children  and  of  the  uncultured — an  evi- 
dence of  an  untrained  mind.     A  rational  will  is  one  that  is 
not  hasty,  waits  for  the  decisions  of  judgment  and  reason, 
and  is  governed  by  the  highest  good   of    the  individual. 
Such  a  will  is  said  to  be  strong  when  it  inflexibly  ministers 
to  the  best  interests  of  the  person,  as  dictated  by  the  de- 
cisions of  the  intellect.     It  is  weak  when  it  permits  itself 
to   be  controlled   by   the   appetites   or  by   any  unworthy 
motives.     The  glutton,  the  tobacco  smoker  and  chewer,  the 
opium-eater,  the  inebriate,  etc.,  have  weak  rational  wills. 
Like  children,  they  are  under  the  domination  of  their  ap- 

38 


The  Will.  39 


petites,  and  the  longer  they  permit  themselves  to  be  thus 
ruled  the  weaker  the  will  becomes. 

98.  When  our  appetites  and  our  passions  gain  the  mastery 
over  us,  they  become  tyrants,  dethrone  the  will,  and  reduce 
us  to  a  state  of  imbecility — pitiable  objects  !     No  one  need, 
however,  be  under  the  power  of  his  appetite  or  controlled 
by  any  debasing  motives.     The  will,  like  other  powers,  can 
be  trained;  but  the  training  must  begin  early  and  continue 
as  long  as  may  be  necessary  for  the  individual  to  acquire 
self-control. 

99.  One  of  the  first  things  a  child  should  be  taught  is  un- 
questionable obedience  to  those  in  authority  over  it.   Besides 
obedience,    neatness    and    cleanliness  of  person,  truthful- 
ness, self-respect,  respect  for  the  rights  of  others,  politeness, 
and  kindness   should   early  be  impressed    upon   its   mind. 
Permitting  a  child  to  have  its  own  way  is  no  kindness  to  it. 
On  the  contrary,  it  is  doing  it  a  lasting  harm.     The  will  is 
trained  by  rigidly  requiring  the  right  to  be  done  and  the 
wrong  to  be  shunned.     In  this  way  right-doing  becomes  a 
habit,  and  this  habit  is  a  right  will. 

100.  Since  the  feelings  urge  the  will,  the  importance  of 
the  formation  of  right  feelings  or  desires  becomes  appar- 
ent; for  if  our  desires  are  in  harmony  with  our  best  judg- 
ment, and  their  force  is  of  sufficient  strength  to  move  the 
will  in  the  same  direction,  we  have  our  powers  under  perfect 
discipline  or  control. 

101.  The  will  is  simply  the  person  willing  or  exercising 
the  power  of  willing.     He  is  at  liberty  to  select  and  to  do 
that  which  will  minister  to  his  well-being,  either  physical  or 
spiritual,  or  that  which  will  prove  destructive  of  it.     The 
will,  therefore,  is  an  important  factor  in  the  formation  of 
character. 

102.  The  power  to  will,  to  select  one  of  several  duties, 
acts,  or  things,  implies  the  ability  or  freedom  to  reject   any 
or  all  of  them,  and  consequently  makes  us  responsible  for 

-^t^f^ 

(UNIVERSITY 


Science  and  Art  of  Education. 


our  acts.  Responsibility  does  not,  however,  apply  only  to 
overt  acts,  but  even  to  thoughts.  This  is  evident  from  the 
fact  that  the  will  can  change  the  subject  of  thought,  or  can 
direct  what  it  shall  be. 

103.  Since  good  conduct  comes  from  good  thoughts  and 
bad  conduct  from  bad  thoughts,  the  importance  of  having 
the  mind  occupied  with  wholesome  thoughts  is  too  plain  to 
require  further  proof. 

REMARK.  —  Here,  again,  the  importance  of  beautiful  surround- 
ings, suitable  associates,  and  wholesome  literature  or  reading- 
matter  becomes  evident. 

104.  Bad  thoughts  can  be  expelled  from  the  mind  only 
by  the  introduction  of  good  ones  —  the  good  will  drive  out 
the  bad,  and   similarly  the  bad  will  drive  out  the  good. 
Here,  again,  we  see  that  we  are  responsible  for  our  thoughts. 

105.  As  before  stated,  the  will  and  the  feelings  depend 
upon  the  intellect.    The  feelings  are  excited  by  the  thoughts, 
and  the  will  is  moved  by  the  feelings.     The  feelings  of  all 
pers.ons  are  not,  however,  excited  with  equal  ease.     Some 
are  moved  very  quickly,  others  very  slowly,  and  between 
these  extremes  many  grades  are   found.     Those  who   are 
easily  or  quickly  excited  are  said  to  be  passionate,  impul- 
sive; they  act  without  proper  consideration,  without  waiting 
for  a  complete  report  or  decision  from  the  intellect.      Rash 
or  impulsive  persons  are  neither  safe  counsellors  nor  safe 
guides;  for  they  frequently  do  things  of  which  they  after- 
wards are  ashamed,  and  for  which  they  are  sorry. 

106.  In  addition  to  the  foregoing  statements  concerning 
the  importance  of  training  the  will  to  depend  upon  the  in- 
tellect for  its  course  of  action,  it  should  be  emphasized  that 
this  dependence  must  be  formed  into  a  habit. 

107.  HABIT.  —  Habits  control  nearly  everything  we  do, 
and  it  is  only  after  we  can  do  a  thing  from  habit  that  we 
can  do  it  with  ease  and  pleasure.     The  use  of  good  lan- 
guage, all  mechanical  executions,  thinking  good  thoughts, 


The  Will.  .  41 


controlling  our  feelings,  and  acting  from  pure  motives  must 
largely  become  matters  of  habit.  Teachers  must  invariably 
insist  upon  such  conduct  from  their  pupils  as  is  reasonable 
and  right  ;  and  this  course  must  be  continued  until  right- 
doing  has  grown  into  a  habit — until  the  pupils  can  be  left 
to  govern  themselves. 

108.  However  necessary  outward  means  of  government 
may  be  during  the  early  periods  of  life,  the  fact  must  not 
be  overlooked  that  they  effect  no  radical  change  in  the  dis- 
position :  they  serve  simply  as  a  restraint.     A  change  of 
disposition  must  come  from  within,  and  must  give  stability 
to  habits  of  doing  right.     Hence  the  further  pupils  advance 
in  intellectual  and   moral  culture — in  their  ability  to  take 
care  of  themselves — the  less  care  need  be  exercised  over 
them  by  parents  and  teachers. 

109.  It  cannot  be  too  deeply  impressed  upon  the  minds 
of  teachers  that  the  best  book  upon  psychology  is  the  liv- 
ing, acting  child.     Child  study,  or  experimental  psychology, 
is  bearing  fruit  for  the  teacher's  guidance  that  speculative 
psychology  never  dreamed  of. 

110.  Teachers  who  desire  to  read  more  to  aid  them  in 
their   studies  than  is    contained    in    the    foregoing   notes 
would  do  well  to  consult  Dr.  W.  O.  Krohn's  "  Practical 
Lessons  in  Psychology  "  and  Prof.  William  James'  "  Briefer 
Course  in  Psychology."     Those  who  wish  to  acquaint  them- 
selves with  the  Herbartian  psychology  and  pedagogy  should 
read  Lange's  "  Apperception "  (edited  by  Dr.  Charles  De 
Garmo),  Dr.  Charles  A.  McMurry's  "  General  Method,"  or 
Rein's  "Outlines  of  Pedagogics." 


IMPORTANT  OBSERVATIONS  AND  INFERENCES. 

1.  Education  begins  and  ends  with  life. 

2.  The  object  of  scholastic  education  is  to  teach  the 
pupil  how  to  learn.     Its  methods  should  therefore  be  such 
as  will   enable  him  to  carry  on  his  own  education  pleas- 
antly and  successfully. 

3.  Education  cannot  create  powers  or  faculties  :  it  can 
only  develop  those  that  exist. 

4.  The  mind  can  develop  what  is  in  itself  only  by  its  own 
activity  ;  self-activity  (exercise),  therefore,  educates. 

5.  The  powers  of  the  child  can  be  exercised  by  no  one 
but  the  child  itself  ;  consequently,  not  what  the  teacher 
does  for  the  child,  but  what  it  does  itself,  educates  it. 

6.  The  inner  promptings  of  the  child  make  themselves 
known  by  outer  manifestations. 

7.  The  child  indicates  its  own  mode  of  receiving  instruc- 
tion: hence  the  teacher  learns  from  the  child  how  to  teach  it. 

8.  It  is  natural  for  a  child  to  seek  knowledge. 

9.  Gratifying  a  child's  desire  for  knowledge  stimulates 
that  desire. 

10.  Knowledge  begins   with  experience  ;    the    concrete 
should  therefore  precede  the  abstract — things  should  pre- 
cede their  signs  or  names. 

11.  Facts  and  phenomena  should  come  before  laws  and 
principles. 

12.  Thought  should  come  before  expression. 

13.  Each  mind  has  its  own  rate  of  growth  and  develop- 
ment. 

42 


Important  Observations  and  Inferences.  43 

14.  Substantial  learning  or  attainments  cannot  proceed 
faster  than  the  mind's  rate  of  growth  and  development. 

15.  Attempting   to    go   too   fast,   or    going   too   slowly, 
weakens  the  mind. 

16.  There  is  an  intimate  relation  between  the  body  and 
the  mind  ;  work  of  either  reduces  the  power  of  the  other. 

REMARK. — Bain,  in  "  Mind  and  Body,"  says  :  "  The  fact  is 
now  generally  admitted  that  thought  exhausts  the  nervous 
substance  as  surely  as  walking  exhausts  the  muscles." 

17.  Rapidly    growing   children    tire   easily  ;    their   rapid 
growth  reduces  their  power  of  endurance. 

18.  "The  time  to  acquire  skill  in  the  use  of  any  power, 
mental  or  physical,  is  when  the  power  is  growing." 

19.  "  The  time  to  teach  a  thing  is  indicated  by  the  arrival 
of  the  child's  interest  in  it.     Children's  interests  change  with 
age.    What  interests  them  at  an  early  period  does  not  do  so 
at  a  later." 

20.  Attention,  memory,  and  imagination  are  not  so  many 
separate  entities,  but  rather  necessary  accompaniments  or 
aids  to  the  other  powers.     We  may  have  as  many  memories 
and  imaginations  as  there  are  classes  of  things  to  remember 
and  to  image,  each  requiring  its  own  peculiar  training. 

21.  Before  a  teacher  charges  his  pupils  with  inattention, 
he  should  ascertain  the  predominating  kind  of  mental  images 
they  form,  whether  visual  or  auditory. 

22.  Poor  remembering    means   in    most   instances   poor 
images  and  understanding,  for  which  teachers  should  largely 
hold  themselves  responsible. 

23.  Before  the  teacher  begins  to  instruct,  he  should  as- 
certain the  contents  of  his  pupils'  minds,  or  he  may  build 
without  a  foundation. 

24.  The  present  must  grow  out  of  and  upon  the  past. 
What  the  child  has   not  experienced  it  cannot  image  or 
comprehend. 

25.  Every  percept  is  made  of  present  and  past  experi- 


44  Science  and  Art  of  Education. 

ences.  All  our  mental  activities  are  performed  with  accu- 
mulated capital  ;  that  is,  every  thought  we  think  receives 
the  benefit  of  all  our  past  thinking.  That  is  apperception. 

26.  Instruction  aims  at  power  and  skill  ;  education  at 
character. 

27.  Adaptation    of    the   subjects  of   instruction   to   the 
pupils'  growing  needs  is  the  key  to  success  in  teaching. 

28.  How  a  subject  is  taught  is  more  important  than  what 
is  taught. 

29.  The   teacher's  life  should  be   an   example   for   his 
pupils,  and  his  success  should  be  measured  by  his  moral 
influence. 

30.  The  end  of  school  government  should  be  self-control 
and  character. 

Herbartianism. — The  five  methodical  steps  which,  ac- 
cording to  Herbart  and  his  disciples,  must  be  taken  in  teach- 
ing a  lesson  :  i.  "  The  preparation  [analysis]  ;  2.  The  pres- 
entation [synthesis;]  3.  The  combination  [association]  ;  4. 
The  recapitulation  [system];  5.  The  application." — Lange's 
Apperception. 


OBJECT-LESSONS. 

A.    THEIR    DESIGN. 

a.  The  training  of  the  senses — observation. 

b.  The  gaining  of  knowledge. 

c.  The  development  of  the  power  of  thought. 

d.  The  cultivation  of  expression. 

B.    THE    PLAN    OR    METHOD    OF    A    LESSON. 

a.  Have  a  well-defined  end  in  view. 

b.  Select  a  suitable  object  to  be  used. 

c.  Determine  the  method  or  order  to  be  pursued. 

d.  Lead  the  pupils  to  make  their  own  discoveries. 

REMARK. — There  is  no  better  way  of  enlarging  the  children's 
vocabulary  and  of  increasing  their  stock  of  knowledge  than  by 
means  of  lessons  on  objects  (things).  With  such  lessons  they 
can  be  taught  the  names,  properties,  relations,  and  parts  of  ob- 
jects. By  "  object-lessons,"  however,  is  meant  lessons  with  ob- 
jects, not  simply  about  them.  The  children  themselves  must 
examine  the  objects.  Knowledge  acquired  in  this  way  is  more 
certain  and  permanent  than  that  which  is  obtained  at  second- 
hand— from  books  or  from  teachers. 

Children  could  profitably  spend  months,  upon  lessons  of 
this  kind  before  receiving  instruction  of  any  other  character. 

45 


PENMANSHIP. 

REMARK. — The  doing  of  anything  is  best  learned  by  intelli- 
gently directed  practice,  and  this  applies  to  nothing  more 
forcibly  than  to  penmanship.  Every  one,  unless  paralyzed  or 
deformed,  can  learn  to  write  a  neat  hand.  The  wretched  writ- 
ing found  in  most  schools  and  among  many  persons  otherwise 
claiming  to  be  educated  is  an  unmistakable  sign  of  defective 
teaching. 

1.  Suggestions. — Proper   position    of  the  body,  correct 
penholding,  and  the  best  work  the  pupils  are  capable  of 
doing,  must  be  insisted  upon  ;  and  all  their  writing,  until  it  is 
as  nearly  perfect  as  they  can  make  it,  should  be  considered 
practice  in  penmanship. 

2.  Every  letter  should  invariably  have  the  same  form, 
that  of  the  so-called  standard  letters. 

3.  Penholding. — The  penholder  should    be  placed  be- 
tween the  thumb  and  the  first  two  fingers,  so  that  it  may  rest 
before  the  third  joint  of  the  forefinger. 

REMARK. — The  penholders  and  pencils  for  children  should, 
if  possible,  be  no  more  than  an  eighth  of  an  inch  in  thickness. 

4.  The  thumb  and  the  fingers  should  be  bent  outward  so 
as  to  bring  the  end  of  the  thumb  opposite  the  first  joint  of 
the  middle  finger. 

5.  To  keep  the  pen  at  the  proper  angle,  the  thumb  should 
be  pressed  a  little  under  the  holder. 

6.  The  left  side  of  the  middle  finger  should  support  the 
holder  just  above  the  pen,  and  the  forefinger  close  over  the 

holder, 

46 


Penmanship.  47 


7.  The  pen  should  be  held  as  lightly  as  possible. 

REMARK. — The  suggestions  on  penholding  apply  equally  to 
the  holding  of  pencils. 

8.  Position  of  the  Body.— The  body  should  be  erect- 
not  resting  on   the  arm   that  carries   the   pen — the   head 
slightly  inclined  forward  to  see  the  writing. 

9.  The  forearm  should  rest  on  the  muscle   in  front  of 
the  elbow  and  the  hand  on  the  nails  of  the  third  and  fourth 
fingers.     The  wrist  should  not  rest  on  the  desk  or  the  paper. 

10.  If  the  hand  is  so  held  that  the  wrist  is  horizontal, 
both  sides  at  equal  distances  from  the  desk,  the  penholder 
will  point  to  the  right  shoulder  and  give  the  right  slant  to 
the  writing. 

11.  To  enable  the  children,  in  their  early  efforts,  to  write 
in  straight  lines,  their  tablets  should  be  ruled  with  base  or 
guide  lines. 

12.  Penmanship  should  be  commenced  with  copying  the 
first  lessons  in  reading,  and  that  a  good  beginning  may  be 
made,  the  teacher  should  show  the  children  how  to  hold  the 
pencils  (or  the  crayon,  if  they  write  upon  the  blackboard), 
and,  when  necessary,  how  to  form  the  letters,  sometimes 
guiding  their  hands. 

13.  Height    of    Letters    and     Spacing — The    propor- 
tionate height  of  the  letters,  and  proper  spacing  of  letters 
and  words,  should  not  be  overlooked. 

14.  Flourishing. — Until   the   pupils   can   write  a   neat, 
plain  hand,  no  efforts  at  flourishing  should  be  tolerated. 

15.  Charts. — Penmanship  charts  should  be  placed  upon 
the  wall  above  the  teacher's  blackboard,  where  the  pupils 
can  at  all  times  see  the  correct  forms  of  the  letters. 

REMARK. — If  the  foregoing  suggestions  on  penmanship  be 
strictly  carried  out,  neither  copy-book  nor  classes  in  writing 
wiil  be  necessary,  and  better  penmanship,  in  less  than  half  the 
present  usual  time,  will  be  the  result, 


PRIMARY  READING. 

1.  INTRODUCTORY  REMARKS. — Before  an  effort  is  made 
to  give  formal  instruction  to  children,  either  in  reading  or 
any  branch  of   knowledge,  their  confidence  and  good  wilj 
must  be  gained.     This  may  be  done  by  engaging  them  in 
conversation  upon  something  that  is  familiar  to  them  and  in 
which  they  take  an  interest.     These  conversations  should 
be  continued  until  the  children's  timidity  has  been  overcome 
and  they  freely  converse  with  the  teacher.     During  these 
familiar  talks  as  much  knowledge  should  be   drawn  from 
them  as  possible.     In  this  way,  too,  the  teacher  can  learn 
the  extent  of  their  stock  of  knowledge,  and  this  informa- 
tion will  serve  him  as  a  basis  for  the  superstructure  of  knowl- 
edge which,  under  his  guidance  and  superintendence,  they 
are  to  rear. 

2.  Reading    is   thinking — not   mere  word-calling ;    con- 
sequently the  more  thoughtful  and  intelligent  the  pupils  are 
made  by  such  preparatory  lessons  as  those  on  objects,  the 
better  they  will  be  prepared  for  reading. 

3.  Reading  may  properly  be  considered  under  two  heads, 
impression  and  expression,  or  silent   reading  and  audible 
reading.     Silent  reading  has  for  its  object  the  getting  of 
thought,  and  audible  reading  that  of  conveying  it  to  others. 
The  getting  of  thought  is  the  first  and  chief  thing  to  be 
aimed  at.     When  this  end  has  been  attained, — the  thought 
found, — conveying  it  to  others  by  means  of  audible  reading 
becomes  comparatively  easy;  for  emphasis,  pause,  and  in- 
flection take  care  of  themselves — the  thought  controls  them. 

48 


Primary  Reading.  49 


4.  Various  methods  of  teaching  beginners  to  read  have 
from  time  to  time  been  advocated  and  practised.     Among 
them  may  be  named  the  alphabetic,  word,  phonic,  and  sen- 
tence.    But  as  no  one  alone  of  these  methods  is  free  from 
objections,  it  is  found  best  to  form  a  method  that  combines 
what  is  best  in  all  of  them. 

5.  The  word  method  seems  to  be  the  simplest,  and  there- 
fore the  best  to  begin  with.     This  method  follows  that  of 
nature,  presenting  wholes  before  parts.     It  is  also  philosoph- 
ical, for,  in  order  to  read,  to  get  the  thought,  words  must  be 
recognized  as  wholes,  each  as  a  single  picture.     If  either 
the  names  or  the  sounds  of  the  letters,  instead  of  the  whole 
words,  attract  the  attention  of  the   pupils,  they  lose  the 
thought,  and  merely  pronounce  the  words. 

REMARK. — Since,  in  order  to  read,  children  must  recognize 
words,  it  is  not  only  reasonable,  but  a  saving  of  time,  to  begin 
with  words. 

6.  Words  with  which  the  children  are  familiar  should  at 
first  be  taught.     The  words  which   they  recognize  through 
the  ear  they  must  now  learn  to  recognize  through  the  eye. 

REMARK. — The  length  of  time  required  to  impress  a  word 
pamanently  upon  the  mind  and  to  make  its  name  of  ready 
recollection  depends  upon  the  interest  with  which  the  teacher 
presents  it.  To  make  this  work  a  success  lie  must  have  a  num- 
ber of  devices  at  ready  command. 

Suggestions  for  Teaching  Primary  Reading.— i.  Select 
a  word  that  is  the  name  of  an  object  in  which  the  children 
take  an  interest.  Engage  them  in  a  conversation  about  the 
object,  to  interest  them,  to  gain  their  attention. 

2.  Write  the  word  upon  the  blackboard.     Tell  them  what 
you   have  written  (its  name)  and  urge  them  to  observe  it 
carefully,  so  as  to  be  able  to  recognize  it  when  they  see  it 
again. 

3.  Erase  it  and  write  it  among  others  vpon  the  black- 
board.    Tell  them  to  find  it. 


50  Science  and  Art  of  Education. 

4.  By  means  of  a  variety  of  exercises  of  this  kind  and  of 
others,  impress  the  word  upon  their  minds,  always  associat- 
ing the  form  (written  word)  with  its  name. 

5.  Test  the  impression  with  word-cards,  charts,  and  any 
other  means  which  you   may  have  at  your  command  or 
which  you  may  be  able  to  devise. 

REMARK. — Writing  the  word  among  others  upon  the  black- 
board affords  a  good  test  of  the  impression. 

6.  To   make   the   impression    permanent,   the    children 
should  be  required  or  urged  to  copy  their  lessons  -both  upon 
the  blackboard  and  into  their  tablets.    The  tablets  used  for 
this  purpose  should  be  ruled,  and  the  lines  should  be  not 
less  than  three  eighths  of  an  inch  apart.     As  before  stated, 
the  pencils  should  be  very  thin — one  eighth  of  an  inch  in 
thickness — to  enable  the  children  to  hold  them  properly. 

7.  Every  lesson  should  begin  with  a  review  of  the  pre- 
ceding lesson  or  lessons.     Every  word  taught  should  be 
reviewed  from  day  to  day  until  it  is  permanently  impressed 
upon  the  mind  and  can  instantly  be  recalled.     The  recog- 
nition of  words  should  be  made  automatic. 

8.  After  the  first  word  has  been  taught,  others  should  be 
taught  to  combine  with  it,  or  should  directly  be  combined 
with  it,  to  form  a  phrase  or  sentence. 

9.  As  many  new  words  should  be  taught  at  each  lesson 
as  the  pupils  can  well  learn. 

10.  The  teacher  should  keep  a  memorandum  of  every- 
thing given  to  the  class,  to  be  used  as  material  for  reviews. 
He  should  also  prepare  as  many  slips  of  paper  with  the 
words  which  the  children  have  learned  written  upon  them, 
as  he  has  pupils.     These  slips  may  be  kept  in  pasteboard 
boxes,    and  whenever   the   children  are   at  leisure — when 
they  have  performed  their  other  tasks,  or  their  assigned 
work — they  should  take  out  the  slips  and  see  how  many  of 
the  words  they  remember. 

11.  The  sentences  written  upon  the  blackboard  as  fead- 


Primary  Reading. 


ing  exercises  may  also  be  copied  upon  slips  of  paper  and 
kept  in  boxes  for  the  children  to  read  after  their  other 
work  has  been  performed. 

12.  Lists  of  the  words  taught  may  be  written  upon  the 
blackboard,  where  the  children  can,  from  their  seats,  see 
them.     Of  these  they  should  be  encouraged  to  make  as 
many  sentences  as  they  can.     The   sentences  should  be 
brought  to  the  class  and  kindly  criticised— errors  pointed 
out  and   improvements  suggested.     These  exercises  train 
children  to  the  correct  use  of  language. 

13.  As  before  stated,  the  words  of  the  reading-lessons 
should  at  first  all  be  taken  from  the  children's  vocabulary, 
or  stock  of  words  in  use. 

14.  The  statements,  or  sentences,  should  as  far  as  pos- 
sible be  about  something  that  interests  the  children.    State- 
ments about  themselves  frequently  prove  interesting  to  them. 

15.  The  teacher  should  have  a  good  supply  of  toy  ob- 
jects.    At  the  recitation  every  member  of  the  class  should 
be  given  one,  and  the  children  encouraged  or  requested  to 
talk  about  them.     Their  talks,  or  sentences,  may  be  written 
upon  the  blackboard  and  read,  or  only  the  most  suitable 
ones  may  be  written  upon  the  blackboard  and  read. 

16.  Number-lessons  may  also  be  made  reading-lessons. 
The  statements  of  facts  which  the  children  make  may  be 
written  upon  the  blackboard  and  read,  or  they  may  write 
them,  at  their  seats,  into  their  tablets,  bring  them  to  class, 
and  read  them. 

17.  Lessons  on  size,  form,  weight,  position,  color,  quality, 
etc.,  may  be  used  in  the  same  manner  and  for  the  same 
purpose  as  those  on  number. 

18.  The  reading  exercises  should  be  varied  from  day  to 
day  ;  that  is,  of  the  same  words  as  many  different  sentences 
should  be  made  as  possible.     Varying  the  exercises   not 
only  lends  interest  to  the  work,  but  helps  to  impress  the 
words  upon  the  children's  minds, 


5  2  Science  -and  Art  of  Education. 

19.  The  sentences  should  at  first  all  be  short.     Long 
sentences  are  too  difficult  for  beginners  ;  their  length  pre- 
vents  the  children   from  readily  grasping   the   contained 
thought. 

20.  The  reading  exercises,  the  words,  phrases,  and  some- 
times  sentences,   may  be    taken  from   a  suitable   book,  a 
Primer  or  First  Reader. 

21.  The  pupils  should  at  first  read  only  from  the  black- 
board ;  afterwards  also  their  own  written  work,  from  their 
tablets,  papers,  or  slates. 

22.  After  the  pupils  have  learned  from  one  hundred  to 
one  hundred  and  fifty  words  by  sight,  by  the  word  method, 
they  should  be  taught   the   analysis  of   words  into  their 
sounds.     They  should   be   shown   that  the  names   of   all 
words  are  made  of  combinations  of  sounds.     This  may  be 
done  by  taking  suitable  words  and  pronouncing  them  slower 
and  slower  each  succeeding  time  until  the  separate  sounds 
are  heard.     Words  in  which  all  the  sounds  may  be  pro- 
longed should  at  first  be  used. 

REMARK. — Some  teachers  introduce  the  sounds  of  the  let- 
ters and  their  signs  almost  from  the  first  lesson  in  reading,  and 
do  it  successfully. 

23.  The  analysis  of  words  into  their  sounds  should  be 
followed  by  the   synthesis  of  the  sounds.     The   children 
should  be  made  acquainted  with  the  letters  that  stand  for 
the  sounds,  and  should  have  practice  in  determining  the 
pronunciation  of  words. 

NOTE. — Teachers  who  desire  a  carefully  worked-out  system 
of  primary  reading,  in  general  accord  with  the  foregoing,  will 
find  "  The  Rational  Method,"  published  by  Silver,  Burdett  & 
Co.,  New  York,  the  most  recent  and  the  best.  It  is  a  thought- 
method,  and  the  shortest  to  the  mastery  of  words  and  intelli- 
gent reading. 

24.  All  words   that   cannot  well  be    taught   by  sounds 
should  be  taught  by  sight,  or  as  wholes. 

25.  The    English   language    contains   about   forty-three 


Primary  Reading.  53 


different  sounds,  and  has  only  twenty-six  letters  by  which 
to  represent  them  ;  some  letters,  therefore,  stand  for  more 
than  one  sound.  The  particular  sound  for  which  a  letter 
stands  is  indicated  by  a  sign  placed  upon  the  letter,  above 
it  or  below  it.  These  signs  are  called  diacritical  marks. 

26.  Whenever  a  letter  is  taught  as  the  representative  of 
a  sound,  its  mark  should  be  taught  in  connection  with  it. 

REMARK. — The  diacritical  marks  enable  the  children  to  dis- 
cover the  pronunciation  of  words. 

27.  Whenever   a  new   word   is   introduced,   its   sounds 
should  be  indicated  by  their  proper  marks.     In  the  dic- 
tionaries the  pronunciation  of  words  is  indicated  by  dia- 
critical marks.     In  some  of  the  first  reading-books  diacriti- 
cal marks  are  also  used. 

Sounds  of  the  vowels  and  consonants  as  given  by  Webster : 

VOWELS. 


i  as  in  ape 

s 

as  in  n6te 

1  "  "  at 

6 

44   "   n6t 

*S  *4   "   arm 

3 

44   44  ^r 

a  44   '4   ask 

6 

44   4'   love 

1  "  "  c3re 

P. 

44   "   mflve 

9  "  44   ftll 

9 

44     "     WQlf 

a  "   "   what 

o 

"   4'   obey 

a  44  44   senate 

03 

44   44   m6^r 

*  44  "  me 

<To 

44   44   book 

5  '4   "met 

u 

"   4<   mute 

2  44   '!   there 

u 

44   44  tip 

*  "   "   terrm 

V 

44   ••   lull 

t  "   '4   thgy 

44   4<   rule 

e  "   44   event 

Q 

44   4<   btirn 

?  "  »  Tee 

- 

44   44   any 

T  "  ••  Tt 
T  *'   "   fTrm 
7  "  4I   pVque 

* 

44   4<   h^mn 
44   44  rrfjfrrh 

CONSONANTS. 

•e    as  in  cat 

a 

as  in  finger 

44   '4   is 

«h  44   44  «horus 

rh' 

44   44   these 

g     "   "   germ 

V 

44   4I  exist 

?     "   "   go 

5  4  Science  and  Art  of  Education. 

28.  As  a  further  aid  to  pupils  in  discovering  the  pro- 
nunciation of  words,  silent   letters  may  be   marked,  also 
double  vowels  and  double  consonants. 

29.  The  names  of  the  letters  of  the  alphabet  afford  no 
aid  to  the  children  in   discovering  the   pronunciation  of 
words ;   they  se,rve  merely  to  designate  the  letters  when 
speaking  of  them,   and   should  therefore  be   taught   only 
indirectly  or  incidentally. 

REMARK. — Oral  spelling  cannot  be  substituted  for  real  spell- 
ing, and  if  practised  at  all,  should  be  postponed  until  it  will 
not  interfere  with  reading. 

30.  To  familiarize  the  pupils  with  the  forms  of  words 
and  to  afford  practice  in  forming  them  and  in  penmanship, 
they  should  be  required  to  copy  carefully  and  neatly,  into 
their  tablets,  either  a  part  or  the  whole  of  every  reading- 
lesson  until  they  have  completed  the  Second  Reader ;  and 
the  tablets  or  books  should  be  preserved  to  note  the  prog- 
ress of  the  pupils  in  penmanship,  spelling,  etc. 

31.  All  new  words  and  words  not  well  known  should  be 
written  upon  the  blackboard,  and  the  pupils  drilled  upon 
them  until  they  can  readily  name  them.     They  should  not 
be  permitted  to  attempt  the  reading  of  a  sentence  until  they 
can,  upon  sight,  pronounce  every  word  in  it. 

32.  Instead  of  being  asked  to  read  a  sentence  or  para- 
graph, they  should  be  requested  to  tell  what  it  says.     They 
should  generally  tell  it  in  their  own  language. 

33.  Conversational   tones   should   be    insisted   upon   in 
reading. 

34.  If  a  lesson  contains  anything  worth  remembering, 
the  pupils  should  (with  some  exceptions)  be  required  to 
give  the  substance  of  it  in  their  own  words.     An  exercise 
of  this  kind  cultivates  their  memory,  imagination,  and  the 
power  of  expression. 

REMARK. — Sometimes,  too,  they  may  be  required  to  substi- 
tute synonymous  words  and  expressions  for  those  found  in 
their  lessons. 


Primary  Reading,  55 


35.  Words  and  sentences  may  be  dictated  to  the  pupils 
to  be  written  into  their  tablets  or  upon  the  blackboard,  to 
test  their  orthography  and  to  impress  the  correct  word* 
forms  upon  their  minds. 

36.  Owing  to  the  similarity  of  the  forms  of  letters,  the 
change  from  script  to  print  is  not  difficult.     To  make  the 
transition,  the  teacher  should  place  exercises  in  both  forms 
of  letters  upon  the  blackboard  and  let  the  children  compare 
them.     A  few  days'  comparison  and  practice   in   reading 
print  will  remove  all  difficulties  in  reading  the  latter. 

37.  As  soon  as  the  children  can,  with  considerable  ease, 
read  from  the  blackboard,  they  should  be  allowed  to  read 
either  from  slips  or  cards  printed  for  the  purpose  or  from 
books ;  and  until  they  can  read  fluently  from  either,  they 
should  have  only  one  or  two  pages  of  reading-matter  given 
them  at  a  time.     If  they  read  from  books,  instead  of  slips 
or  cards,  they  should  be  given  them  only  during  the  recita- 
tion. 

REMARK. — If  the  foregoing  suggestions  with  reference  to 
reading  from  slips  or  cards  and  books  be  carefully  observed,  the 
children  will  every  two  or  three  days  receive  something  new  to 
read,  and  the  expectation  of  this  will  keep  up  their  interest  in 
reading. 

38.  The  sentences   should  at  first  be  commenced  with 
small  letters,  and  each  letter  should  invariably  have  the 
same  form — that  of  the  so-called  standard  letters. 

REMARK. — The  teacher  cannot  be  too  careful  with  his  own 
penmanship.  As  it  is  to  be  an  example,  a  guide,  to  his  pupils, 
it  should  as  nearly  as  possible  be  perfect. 

39.  As  soon  as  it  is  believed  not  to  confuse  the  pupils, 
the  capital  letters  should  be  introduced  to  begin  sentences. 

40.  The  pupils  may  read  three,  four,  or  more  months  only 
from  the  blackboard  and  their  tablets  or  papers. 

41.  Only  one  thing  should  be  introduced  at  a  time,  and 
the  teacher  should  be  sure  that  it  is  both  understood  and 
remembered  before  he  introduces  anything  else. 


56  Science  and  Art  of  Education. 

42.  Nothing  less  than  the  best  work  the  pupils  are  capa- 
ble of  preparing  should  be  accepted  from  them.    Accepting 
carelessly  prepared  work  tends  to  the  formation  of  careless 
habits. 

43.  All  the  teacher's  work  should  be  an  example  for  his 
pupils. 

44.  Articulation  needs  careful  attention  in  every  exercise 
in  which  the  voice  is  used. 

45.  After  the  pupils  are  far  enough  advanced  to  do  so, 
they  may  be  required  to  find  all  the  possible  meanings  of 
which  a  sentence  permits  by  emphasizing  in  succession  the 
different  words  in  it. 

46.  The  children  should  as  early  as  possible  read  for  in- 
formation, so  that  a   desire   for   reading   may  be  formed. 
Much  of  the  reading  done  in  the  majority  of  schools  adds 
nothing  to  the  pupils'  stock  of  knowledge,  neither  possesses 
any  interest  for  them,  and  consequently,  in  a  correct  peda- 
gogic sense,  does  more  harm  than  good. 


ADVANCED  READING. 

REMARK  i.— Primary  reading,  as  the  term  is  used  in  these 
Notes,  refers  to  that  done  on  the  blackboard  and  in  the  "  First 
Reader." 

REMARK  2.— If  reading  is  well  taught  in  the  primary  grade  or 
class,  that  of  the  higher  will  largely  take  care  of  itself. 

1.  The  reading-matter  for  children  should,  as  far  as  pos- 
sible, be  of  a  thought-stimulating,  interest-creating  charac- 
ter, adapted  to  their  comprehension   and  power  of  appre- 
ciation.     Much  that  is  now  read  in  the  schools  falls  far 
short  of  meeting  these  conditions. 

2.  As  has  already  been  stated,  but  will  bear  repetition,  a 
child  should  not  be  permitted  to  read  a  sentence  audibly 
until  it  has  read  it  silently,  and  has  obtained  the  thought. 
In  other  words,  it  should  not  be  allowed  to  express  the 
thought  until  it  has  it.     Permitting,  or,  as  is  too  frequently 
done,  requiring,  pupils  to  read,  to  express  thoughts  audibly 
before  they  have  any — thoughtless  reading — is  chiefly  re- 
sponsible for  the  poor  reading  that  is  so  general  in   all 
grades  of  schools. 

3.  Thought-getting  and  thought-expressing  are   not  the 
same.     A  pupil  may  make  commendable  progress  in  obtain- 
ing thought,  but  be  slow  in  expressing  it.     Words  are  slow 
in   impressing  themselves  upon   some   minds.     There  are 
children,  too,  who  learn  more  readily  through  the  ear  (ear- 
minded)  than  through  the  eye  ;  they  remember  better  what 
they  hear  than  what  they  see.     Instead,  therefore,  of  chid- 
ing or  scolding  them  for  slowness,  the  teacher  should  ascer- 
tain its  cause  and,  as  far  as  possible,  provide  a  remedy. 

57 


5  8  Science  and  Art  of  Education. 

4.  When  pupils  are  far  enough  advanced  to  do  so,  they 
should,  frequently  at  least,  if  not  generally,  be  required  to 
read  a  paragraph  or  selection  silently,  and  then  give  the 
thought    in    their  own    words,    orally  or  in  writing.     This 
method  of  teaching  reading  cultivates  both  thought  and  ex- 
pression, and  consequently  has  a  greater  culture  value  than 
reading  as  it  is  usually  taught. 

REMARK. — Good  or  expressive  reading  should  be  insisted 
upon  in  every  class  or  subject  in  which  a  pupil  is  required  to 
read. 

5.  Pronunciation. — (a)  Careless  or  slipshod  pronuncia- 
tion seems  to  be  the  rule  rather  than  the  exception  in  the 
majority  of  schools.     It  is  not  an  uncommon  thing  to  hear 
such  pronunciations  as  the  following:  Fir  ior  for,  ben  for 
been,  uf  for  of,  sence  for  since ,  sepret  for  separate,  evry  for 
every,  rhetric  for  rhetoric,  generly  for  generally,  easlyim  easily, 
practus  for  practice,  calm  for  calm,  kin  for  can,  blessid  for 
blessed,  goen  for  going,  govner  for  governor,  histry  for  history, 
cave  for  carve,  staum  for  storm,  articlation  for  articulation, 
peticular  f or  particular,  prinsple  ion  principle,  artic  for  arctic, 
ax  for  acts,  plitical  im  political,  an  for  and,  dag  for  dog,  four t 
for  fourth,  you-ri-zon-nears  for  your  eyes  and  ears,  hi-zoiv-ry- 
zup  for  his  hour  is  up,  tay-cary  for  take  care,  gavim  for  gave 
him,  ovis  for  of  his. 

(£)  When  errors  like  the  foregoiqg  have  been  hardened 
into  habits  they  are  difficult  to  eradicate ;  but  they  can  be 
corrected  by  persistent  daily  practice  on  the  vowels  and 
consonants,  first  separately  and  afterwards  in  combination. 
A  part  of  every  instruction  period,  as  long  as  necessary, 
should  be  devoted  to  phonic  drills. 

(c)  A  reader  or  speaker  can  make  himself  more  easily 
understood  by  a  correct  and  clear  enunciation  of  his  vowels 
and  a  distinct  articulation  of  his  consonants  than  either  by 
•  a  high  pitch  or  by  loudness. 

6.  Emphasis. — (a)    Any  method   of  giving  special  sig- 


Advanced  Reading.  5  9 


nificance  to  an  expression  is  emphasis,  and  emphasis  is  the 
life  of  reading.  Correct  emphasis  helps  the  hearer  to  the 
meaning  of  what  is  read,  and  incorrect  conceals  it,  or 
hinders  him  from  getting  it.  A  knowledge  of  the  leading 
principles  of  emphasis  is  therefore  a  necessity  to  good 
reading. 

(b)  Alexander  Melville  Bell,  one  of  the  highest  authori- 
ties on  expressive  reading  and  speaking,  says:  "  The  laws  of 
emphasis  form  a  study  of  the  highest  intellectual  value, 
which  has  been  too  little  investigated  and  systematized. 
No  other  department  of  elocution  can  compare  with  this  in 
importance  ;  yet  not  only  has  it  been  superseded  in  books 
by    unnecessary    rules    for  inflection,  and    in    schools    by 
thoughtless   imitation,    but   these  rules,  and   all   exercises 
founded  on  them,  constantly  violate  the  laws  of  (rhythmic) 
accent.     Here  is  one  point  in  which  almost  absolute  uni- 
formity must  prevail  among  all  good  readers.     Set  practice 
right  in  respect  to  emphasis,  and  inflection  cannot  go  far 
wrong." 

(c)  The  sense  of  what  is  read  determines  the  emphasis  to 
the  reader,  and  the  emphasis  conveys  it  to  the  hearer. 

(d)  Misplaced  emphasis  perverts  the  meaning.     Take  the 
following,  for  example,  and  read  it  as  here  indicated  by  the 
italics,  and  as  it  is  generally  read,  and  note  the  sense:  "  In 
the  beginning  was  the  Word,  and  the  Word  was  with  God, 
and  the  Word  was  God."     This  rendering  would  lead  us  to 
believe  that  nothing  existed  in  the  beginning  but  the  Word, 
and  that  at  that  early  period,  at  least,  it  was  God,  but  that 
at  a  later  day  it  was  changed  to  something  else. 

Read  the  foregoing  as  here  indicated,  and  observe  the 
difference:  "  In  the  beginning  was  the  Word,  and  the  Word 
was  with  God,  and  the  Word was  God." 

(e)  The  fifth  verse  of  the  first  Psalm  is  frequently  read  : 
"  The  ungodly  are  not  so  ;  but  are  like  the  chaff  which  the 
wind  driveth  away." 


60  Science  and  Art  of  Education. 

Without  saying  anything  about  the  accent  on  godly  in 
ungodly,  this  reading  permits  of  at  least  two  meanings  :  i. 
That  there  are  two  kinds  of  chaff — one  driven  by  the  wind, 
which  the  ungodly  resemble;  the  other  not  so  driven,  which 
we  may  infer  the  godly  are  like.  2.  That  one  kind  of  chaff 
is  driven  by  the  wind,  the  other  by  something  else. 

(/)  In  Acts  20  :  16  is  found  a  good  example  to  illustrate 
the  variety  of  meanings  of  which  a  sentence  permits  by 
changing  the  place  of  emphasis. 

1.  Paul  had  determined  to  sail  by  Ephesus. 

2.  Paul  had  determined  to  sail  by  Ephesus. 

3.  Paul  had  determined 'to  sail  by  Ephesus. 

4.  Paul  had  determined  to  sail  by  Ephesus. 

5.  Paul  had  determined  to  sail  by  Ephesus. 

6.  Paul  had  determined  to  sail  by  Ephesus. 

The  first  sentence  states  Paul's  determination  ;  the  sec- 
ond, what  it  had  been  ;  the  third,  that  his  mind  had  been 
fully  set;  the  fourth,  that  he  meant  to  go  by  water;  the  sixth, 
the  route — by  way  of  Ephesus. 

REMARK.— Requiring  children,  or  even  more  advanced 
pupils,  to  read  all  the  various  meanings  of  which  a  sentence 
permits  by  shifting  the  place  of  emphasis,  is  one  of  the  best 
ways  of  breaking  up  monotonous  reading. 

For  this  purpose  a  sentence  like  the  following  may  some- 
times be  used  in  connection  with  their  regular  reading  ex- 
ercises :  Did  you  see  Henry  this  morning  ? 

(g)  The  following  are  given  in  some  reading-books  as 
examples  of  the  use  of  the  circumflex,  but  the  efforts  that 
are  usually  made  to  read  them  are  in  few  instances  success- 
ful. Properly  applied  emphasis,  however,  removes  the 
difficulty,  sets  the  inflections  right,  and  expresses  the  in- 
tended sense. 

A  man  who  is  in  the  daily  use  of  ardent  spirits,  if  he  does 
not  become  a  drunkard,  is  in  danger  of  losing  his  health  and 
character. 


Advanced  Reading.  6 1 


Stress  upon  not  makes  good  sense  ;  but  if  placed  upon 
drunkard  it  would  make  inebriety  a  necessity  to  the  preser- 
vation of  health  and  character. 

The  dog  would  have  died  if  they  had  not  cut  off  his 
head. 

Stress  upon  not  expresses  the  sense,  but  if  placed  upon 
both  died  and  head,  we  would  be  told  that  cutting  off  his 
head  saved  his  life. 

(h)  The  kind  of  emphasis  depends  upon  the  kind  of 
thought  to  be  expressed. 

7.  Pausing. — (a)  Pauses,  or  cessations  of  the  voice,  are 
required  in  reading  to  enable  the  hearer  the  better  to  grasp 
the  meaning  of  what  is  read. 

(b)  The  pauses  are  governed  by  the  sense  and  not  by  the 
punctuation-marks  ;    hence,   though    cessations    generally 
occur  at  these  marks,  they  are  also  required  where  such 
points  would  be  out  of  place. 

(c)  In  the  examphs  which  follow  pauses  are  indicated  by 
the  dash. 

(d)  Now — about  that  time — Herod — the  king — stretched 
forth  his   hands — to   vex — certain   of   the   church.     (Acts 
it:  i.) 

The  omission  of  the  pause  after  Herod  would  signify  that 
one  of  several  persons  by  that  name  is  meant. 

The  pause  after  to  vex  might  be  omitted,  but  its  use  adds 
force  to  the  expression. 

(e)  But — the  Jews  which   believed   not,  —  moved   with 
envy, — took  unto  them  certain  lewd  fellows — of  the  baser 
sort.     (Acts  17:5.) 

Read  without  a  pause  after  Jews,  conveys  the  sense  that 
those  of  the  Jews  who  believed  not  were  moved  with  envy; 
and  with  the  pause,  that  none  of  them  believed.  A  pause 
might  also  be  made  after  them,  but  its  omission  does  not 
add  uncertainty  to  the  meaning. 


62  Science  and  Art  of  Education. 

(/)  There  was  a  man  sent  from  God, — whose  name  was 
John.  (John  i  :  6.) 

The  omission  of  the  pause  after  God  might  convey  the 
meaning  that  the  man  was  sent  from  the  God  whose  name 
was  John. 

(g)  And — turning  the  cities  of  Sodom  and  Gomorrha  into 
ashes — Condemned  them.  (2  Peter  2  :  6.) 

And,  the  first  word,  belongs  to  condemned  (in  reading),  not 
to  turning,  and  this  the  pauses  serve  to  show. 

8.  Grouping.— (a)  Words  are  spoken  either  singly  or  in 
groups.  Those  that  express  a  unit  of  thought  must,  by  the 
voice,  be  grouped  into  a  unit  of  expression,  and  read 
throughout,  without  interruption,  in  the  same  tone  as  if  they 
were  one  word. 

(fr)  In  the  following  examples  the  grouped  words  are 
placed  within  brackets: 

(c)  Forasmuch  then  as  the  children  are  [partakers  of 
flesh  and  blood],  he  also  himself  likewise  [took  part  of  the 
same];  that  through  death  he  might  destroy  [him  that  had 
the  power  of  death],  that  is,  the  devil.  (Hebrews  2  :  14.) 

Each  of  the  expressions  within  brackets  may  be  regarded 
as  equivalent  to  a  word. 

(a)  I  charge  thee  therefore  before  God,  and  the  Lord 
Jesus  Christ,  [who  shall  judge  the  quick  and  the  dead  at  his 
coming];  preach  the  word.  (2  Timothy  4  :  i,  2.) 

The  clause  within  brackets  is  subordinate  to  what  follows 
(preach  the  word),  and  this  must  be  made  manifest  in  read- 
ing, by  grouping  and  tone  of  voice. 

(e)  [Men  shall  buy  fields  for  money,  and  subscribe  evi- 
dences, and  seal  them,  and  take  witnesses  in  the  land  of 
Benjamin,  and  in  the  places  about  Jerusalem,  and  in  the 
cities  of  Judah,  and  in  the  cities  of  the  mountains,  and  in 
the  cities  of  the  valley,  and  in  the  cities  of  the  south]:  for 
I  will  cause  their  captivity  to  return,  saith  the  Lord. 
(Jeremiah  $2  \  44.) 


Advanced  Reading.  63 


The  substance  of  all  within  the  brackets  is,  that  pros- 
perity shall  again  return  to  the  land. 

9.  Etymology. — Etymology  should  receive  attention  in 
connection  with  reading. 

REMARK  i. — A  good  reader  reads  thoughts,  not  words.  He 
pictures  to  himself  his  author's  views  and  expresses  them  as  if 
they  were  his  own.  He  is  unconscious  of  everything  but  the 
thought.  If  pronunciation,  inflection,  holding  of  book,  posi- 
tion of  feet  or  hands,  or  anything  else,  diverts  his  attention,  he 
loses  the  thought  and  reads  like  a  machine. 

REMARK  2. — Reading  cannot  be  taught  by  rules ;  it  requires 
a  competent  teacher,  one  who  can  himself  read  and  teach,  and 
who  can  discriminate  between  the  useful  and  the  useless. 

Teachers  who  desire  to  become  effective  readers,  but  can- 
not avail  themselves  of  the  services  of  a  competent  in- 
structor, will  find  Alexander  Melville  Bell's  "  Principles  of 
Elocution  "  an  excellent  work  for  self-help. 


NOTES  AND  SUGGESTIONS  ON  TEACHING  THE  ENG- 
LISH LANGUAGE. 


CHAPTER  I.  GENERAL  CONSIDERATIONS. 

1.  Like  all  other  languages,  that  of  the  English-speaking 
people  conforms  to  laws,  and  these  laws  are  laid  down,  or 
taught,  in  books  on  English  grammar. 

2.  The  laws,  or  principles,  of  grammar  are  inductions 
from  a  study  of  the  mechanism  of  the  language  ;  and,  like 
those  of  the  material  universe,  are  not  made,  but  discov- 
ered. 

3.  The  laws  of  language,  as  found  in  books  on  grammar, 
rhetoric,  and  logic,  may  be  pursued  by  themselves  as  sci- 
ences, or  they  may  be  introduced  as  they  are  needed  to  en- 
able the  student  to  acquire  a  correct,  an  intelligent,  and  a 
skilful  use  of  the  language. 

4.  Prof.  W.   D.   Whitney,  in   his    Essentials   of  English 
Grammar,  says  :  "  It  should  be  a  pervading  element  in  the 
whole   home  and  school  training  of  the  young,  to  make 
them  use  their  own  tongue  with  accuracy  and  force  ;  and 
along  with  any  special  drill  directed  to  this  end,  some  of 
the  rudimentary  distinctions  and  rules  of  grammar  are  con- 
veniently taught.     But  that  is  not  the  study  of  grammar, 
and  it  will  not  bear  the  intrusion  of  much  formal  grammar 
without  being  spoiled  for  its  own  ends.     It  is  constant  use 
and  practice,  under  never-failing  watch  and  correction,  that 

64 


General  Considerations.  65 

makes  good  writers  and  speakers  ;  the  application  of  direct 
authority  is  the  most  efficient  corrective.  Grammar  has  its 
part  to  contribute,  but  rather  in  the  higher  than  in  the 
lower  stages  of  the  work.  One  must  be  a  somewhat  re- 
flective user  of  the  language  to  amend  even  here  and  there 
a  point  by  grammatical  reasons  ;  and  no  one  ever  changed 
from  a  bad  speaker  to  a  good  one  by  applying  the  rules  of 
grammar  to  what  he  said." 

5.  From  the  foregoing  it  seems  clear  that  a  distinction 
must  be  made  between  acquiring  the  skilful  use  of  a  lan- 
guage and  the  study  of  its  mechanism.     The  former  comes 
from   practice,  under  careful  supervision,  and  is  an  art  ; 
the  latter  is  the  result  of  study,  and  is  a  science.     The  sci- 
ence and  the  art  of  language  are  therefore  different  things, 
and  are  pursued  for  different  ends. 

6.  The   advocates   of   technical   grammar  as   a  general 
school  study  but  a  few  years  ago  claimed  that  it  teaches 
its  learners  to  speak  and  to  write  the  English  language  cor- 
rectly.    When,  however,  it  was  asserted  by  those  who  had 
given   the  subject  earnest  consideration,  that  it  failed  to 
prove  its  claims,  its   advocates  maintained  that  its  short- 
comings must  be  attributed  to  the  teaching,  and  not  to  the 
subject.     But  this  ground  having,  both  by  experience  as 
well  as  by  a  careful  study  of  the  subject,  been  found  unten- 
able, has  now  been  abandoned  by  the  foremost  thinkers 
and  students  of  education. 

7.  Since,  therefore,  it  has  been  found  that  the  study  of 
English  grammar  does  not,  in  fact  cannot,  make  good  writ- 
ers and  speakers,  much  less  importance  is  placed  upon  it 
than  formerly. 

8.  Under  the  topic  of  Grammar  in  City  Schools,  Vol.  I 
of  the  Report  of   1888-89,  of  Dr-  w-  T-  Harris,  Commis- 
sioner of  Education,  has  the  following  in  agreement  and 
confirmation  of  the  foregoing,  viz. :  "  In  the  admitted  fact 
that  the  formation  of  habits  of  correct  speech  is  not  de- 


66  Science  and  Art  of  Education. 

pendent  upon  a  knowledge  of  the  rules  and  definitions  rela- 
tive to  the  construction  of  language  and  their  mutual  de- 
pendence, is  found  the  justification  for  the  lessened  weight 
attached  to  such  study." 

The  Report  quotes  the  following  from  Fitch's  Lectures 
on  Teaching  :  "  The  practical  art  of  using  language  in 
speech  or  writing  with  good  taste  and  correctness  .  .  . 
is  probably  best  to  be  attained  by  talking  to  the  pupil,  by 
taking  care  that  he  hears  little  but  good  English,  by  cor- 
recting him  when  he  is  wrong,  by  practising  him  much  in 
writing,  and  when  he  makes  a  mistake,  by  requiring  him  to 
write  the  sentence  without  one.  It  will  certainly  not  be 
attained  by  setting  him  to  learn  Murray's,  or  indeed  any 
other  grammar." 

The  article  on  the  study  of  grammar  closes  with  the  fol- 
lowing important  statement,  viz.:  "The  art  is  the  thing 
directly  useful  :  the  science  has  no  obvious  relation  to 
practical  affairs.  The  ability  to  speak  and  write  correctly 
is  not  only  desirable,  but. essential  in  every  walk  of  life; 
the  technical  rules  of 'etymology  and  syntax  are  almost  val- 
ueless in  themselves.  Therefore,  in  accordance  with  the 
movement  whose  progress  is  here  recorded,  the  art,  that  is, 
the  practical,  increases  in  importance  in  the  course  of 
study,  while  the  science,  that  is,  the  disciplinary,  decreases 
in  the  same  proportion." 

9.  It  is  true  that  formal  or  technical  grammar  has  some 
disciplinary  value,  but  the  amount  of  it   is  usually  greatly 
overstated,  and  unfortunately  so,  for  much  of  this  supposed 
value   is  responsible  for  the  sad  condition  in  which  the 
study,  if  it  may  be  so  called,  leaves  the  minds  of  the  chil- 
dren who,  reluctantly,  spend  their  time  upon  it. 

10.  Instead  of  dividing  the  study  of  language  into  gram- 
mar, rhetoric,  and  logic,  and  pursuing  each   as   a  separate 
subject,  all  should  be  taught  under  the   head  of  language, 
and  each  at  the  proper  time  made  to  contribute  its  share  tQ 


General  Considerations.  67 

"the  perfection  of  the  whole,  namely,  the  correct,  elegant, 
and  forcible  use  of  it  in  writing  and  speaking. 

REMARK. — The  last  paragraph  refers  to  the  work  of  schools 
below  the  college. 

11.  The  use  of  good  language  must  become  a  habit — 
"  an  unconscious  one."     But  habits  are  of  slow  formation  ; 
that  of  language  requires  years.     A  correct  taste,  the  ability 
to  form  a  correct  judgment  of  a  composition,  must  be  ac- 
quired.    Like  misspelled  words,  badly  constructed  language 
must  offend  the  taste  ;  that  is,  its  defects  or  faults  must  at 
once  appear  on  Jpeing  seen  or  heard.     No  one,  therefore, 
whose  taste  is  uncultivated  can  teach  language.     He  may 
be  able  to  teach  grammar,  and  to  some  extent  rhetoric  and 
logic  ;  but  he  cannot  tell  whether  discourse,  of  whatever 
kind,  is  well  constructed,  and  therefore  can  be  of  no  ser- 
vice to  learners  in  the  formation  of  taste,  or  in  acquiring 
the  use  of  good  language. 

12.  From   the  foregoing  considerations   the   conclusion 
seems  evident  that  language  should  be  taught  by  practice, 
intelligent  practice,  upon  the  principle  that  we  learn  to  do 
a  thing  by  doing  it,  and  not  by  merely  learning  about  doing 
it. 

REMARK. — As  before  stated,  all  the  technical  grammar  nec- 
essary to  a  correct,  forcible,  and  intelligent  use  of  English  not 
only  can  be  acquired  in  connection  with  reading  and  composi- 
tion, but  should  be  so  acquired. 


CHAPTER  II. 

I.  ORAL  LANGUAGE. 

REMARK. — Spelling,  penmanship,  punctuation,  and  capitali- 
zation belong  to  composition,  and  should  be  taught  in  co'nnec- 
tion  with  it,  and  not  as  separate  branches  of  study. 

1.  In    order   that    children    may    talk,«they    must    have 
something  to  talk  about  ;  that  is,  they  must  have  a  subject 
for  conversation. 

2.  The  subject  should  be  one  that  will  interest  them  and 
that  will  add  to  their  stock  of  knowledge.     Stories  that  add 
nothing  to  their  knowledge,  that  do  not  improve  their  pow- 
ers of  observation  and  thought,  or  contain  anything  worth 
remembering,  should  generally  be  avoided. 

3.  The  subject  should  be  one  that  the  children  under- 
stand, or  can  readily  be  led  to  understand.     It  should  gen- 
erally be  one  which  they  have  observed  or  can  observe.     It 
should  be  thoroughly  understood  by  them.     Half  knowl- 
edge is  little  better  than  none  at  all. 

REMARK. — Conversation  depends  upon  observation,  memory, 
imagination,  and  discrimination. 

4.  Nothing  would   be  lost,  but  considerable  gained,   if 
children    had  exercises    in    observation    and    conversation 
some  weeks,  or  even  months,  before  they  begin  to  read. 

5.  All    their  lessons   furnish   material   for   conversation. 
No  teacher  need  be  at  a  loss  for  material,  for  he  has  the 
whole  animal,  vegetable,  and  mineral  kingdoms  from  which 
to  select.     Judgment    must,  however,  be   exercised  in  the 
selection  and  in  the  order  of  presentation.     The  simplest 
and  most  interesting  to  children  should  come  first,  and  then 

63 


General  Considerations. 


there   should   be   a  regular    gradation    in   the   order   best 
adapted  to  the  growth  and  development  of  their  minds. 

6.  The  most  interesting  objects  for  children  are  living 
things,  animals.     Those  with   which   they  seem    best   ac- 
quainted, and  which  they  can   the  more   readily  examine 
and  study,  should  come  first.     The  cat,  dog,  cow,  horse, 
pig,  sheep  ;  chickens,  ducks,  geese,  turkeys,  pigeons,  par- 
rots, canary-birds,  are  not  only  interesting  but   profitable 
objects  for  observation  and  study.     Notwithstanding  that 
we  seem  to  be  familiar  with  them,  to  our  discredit  it  must 
be  said,  we  know  little  about  them.     Children  should  be 
led  to  study  them,  and  conversations  about  them  will  in 
the  best  way  lead  to  this. 

REMARK. — This  kind  of  language  work  will  require  the 
teachers  to  familiarize  themselves  with  the  objects  which  the 
children  are  studying,  and  will  thus  at  the  same  time  enlarge 
their  own  sphere  of  knowledge. 

7.  Flies,  bees,  wasps,  spiders,  butterflies,  bumblebees,  all 
suitable  kinds  of  insects,  worms,  birds,  etc.,  found  in  the 
community,  afford  suitable  material  for  observation,  study, 
and  conversation. 

8.  The  vegetable  kingdom   should  also  be  drawn  upon. 
Roots,  stems  or  stalks  (or  trunks),  leaves,  flowers,  and  seeds 
should  be  observed  ;  their    similarities  and  dissimilarities 
noticed,  and  their  uses  discussed.     Plants  about  home,  in- 
cluding grasses   and  trees,  should  first  receive  attention  ; 
and  it  cannot  be  too  deeply  impressed  upon  the  minds  of 
the  teachers  that  the  things  themselves,  and  not  pictures  or 
descriptions  of  them,  are  to  be  the  objects  of  observation 
and  study.     Plants  may  be  kept  in  pots  in  the  windows  or 
other  places  of  the  school-room.     Towards  spring,  twigs 
may  be  cut  from  trees,  and,  in  jars  partly  filled  with  water, 
placed  in  the  windows  where  they  will  be  in  the  sun,  and 
the  opening  of    their    buds    observed    from  day   to  day. 
Seeds  may  be  studied  in  the  fall  of  the  year.     Towards 


70  Science  and  Art  of  Education. 

spring  they  may  be  planted  in  "  shallow  boxes,  saucers,  or 
any  other  convenient  vessels  rilled  with  moist  earth,  sand, 
or  saw-dust."  They  may  also  be  planted  on  cotton  and 
other  suitable  material  floating  upon  water  in  wide-necked 
bottles,  or  they  may  be  put  into  a  sponge  placed  in  a  saucer 
of  water.  In  this  way  their  germination,  the  growth  of  the 
root,  stem,  etc.,  may  readily  daily  be  observed  and  noted. 

9.  The  various  kinds  of  minerals,  including  earths  and 
stones,  can  also  be  made  a  profitable  study,  and  therefore 
afford  good  material  for  conversation. 

REMARK.-— Jackman's  Nature  Studies,  published  by  Henry 
Holt  &  Co.,  New  York,  is  a  book  of  valuable  suggestions. 

10.  Conversations  may  be  had  about  things  in  the  school- 
room, on  the  school-grounds;  appearance  of  the  sky,  kinds 
of  clouds,  direction  of  winds  and  their   effect   upon   the 
weather.     Things  at  home,  such  as  may  be  found  in  the 
sitting-room,  the  parlor,  on  the  table,  in  the  kitchen,  the 
laundry,  the  pantry,  the  cellar,  the  barn,  on  the  farm,  etc., 
may  also  be  used. 

11.  The  children  should  have  opportunities  to  learn  and 
to  tell  how  the  various  kinds  of  business  of  a  community 
are   conducted.      They  should  name  the  kinds  of  stores  ; 
tell  what  is  sold  in  them  ;  where  and  how  the  goods  are 
procured  ;  in  what  ways,  where,  and  upon  what  terms  they 
are  bought  ;  also  upon  what  terms  generally  sold  ;  and  the 
necessity  of  such  places  of  business.     The  post-office,  ex- 
press-office, bank,  court-house,  jail,  railroad,  railroad  station, 
should  be  explained  and  discussed.     Their  advantages  or 
necessities,  as  the  case  may  be,  should  form  part  of  the  dis- 
cussion.    In  the  same  way  may  the  Sunday-school  and  the 
church  be  used  and  their  influence  upon  the  community  be 
brought  out.     The  various  town  and  township  officers,  their 
necessity,  duties,  and  how  they  are  elected,  installed,  and 
paid,  will  at  the  same  time  be  lessons  in  civil  government. 


General  Considerations.  7 1 

REMARK.— What  the  children  do  not  know  the  teachers  must 
tell  them. 

12.  Events  of  the  day  that  are  within  the  children's 
comprehension,  and  in  which  they  can  be  interested,  should 
be  used  for  oral  language  work. 

REMARK.— As  will  have  been  observed,  the  foregoing  mate- 
rial for  conversation  is  designed  to  make  the  children  ac- 
quainted with  their  surroundings,  and  to  make  them  observant, 
thoughtful,  and  intelligent. 

II.  WRITTEN  LANGUAGE. 

REMARK  i. — All  the  material  suitable  for  oral  language  is 
equally  so  for  written  work  ;  and  as  soon  as  the  pupils  can  use 
the  pen  or  pencil  they  should  be  encouraged  to  talk  with  it,  or, 
in  other  words,  to  write  their  thoughts,  or  at  least  some  of 
them.  Copying  well  written  extracts  and  writing  from  memory, 
are  good  language  exercises,  occasionally  to  be  used  with  be- 
ginners. 

REMARK  2.— Besides  the  regular  daily  lessons  in  the  various 
branches  of  study,  which  should  all  at  the  same  time  be  re- 
garded as  lessons  in  language,  the  following  exercises  and  sug- 
gestions, if  intelligently  used,  will  aid  the  teacher  in  training 
his  pupils  to  the  writing  of  good  English. 

1.  Relate  something  of  interest  to  them  and  let  them  re- 
produce it  in  their  own  words. 

2.  Read  short,   easy,  but  complete  extracts,  stories,  or 
items  of  news,  to  them,  and  let  them  give  the  substance  in 
their  own  words. 

3.  Let  them  say  what  they  saw  on  their  way  to  school,  to 
the  post-office,  the  store,  the  church,  etc. 

4.  Let  them  write  the  history  of  an  hour,  a  day,  a  week, 
a  month,  etc. 

5.  Let  them  write  a  narration  of  a  walk,  a  ride,  a  real  or 
an  imaginary  journey,  a  picnic,  party,  sociable,  or  anything 
that  has  occurred  of  which  they  have  knowledge,  or  which 
they  imagine  as  having  occurred. 

6.  Let  them  describe  a  room,  house,  barn,  stable,  school- 
house  ;  the  post-office,  court-house,  church  ;  a  chair,  table, 


72  Science  and  Art  of  Education. 

bench,  door,  window,  knife,  pair  of  scissors,  thimble,  look- 
ing-glass, clock,  stove,  wash-stand,  comb,  brush,  sewing- 
machine,  hat,  cap,  desk,  tree,  fence,  gate,  wagon,  wheelbar- 
row, shovel,  fork,  hammer,  broom,  horse,  cow,  dog,  cat,  rat, 
mouse,  pig,  sheep,  fly,  spider,  caterpillar,  beetle,  plant,  flower ; 
in  short,  anything  that  admits  of  description  and  that,  in 
the  judgment  of  the  teacher,  is  not  beyond  their  ability. 

7.  Let  them  compose  (make)  problems  ;  also  write  out 
solutions  of    problems  ;  sometimes    all  in  words,  without 
figures. 

8.  Let  them  name  and  describe  articles  of  clothing  and 
the  materials  of  which  they  are  made. 

9.  Let  them  write  what  they  know  of  the  school  district, 
township,  town,  county,  state,  other  states,  countries,  etc. 
These  exercises,  like  the  preceding,  will  serve  the  double 
purpose  of  knowledge  and  language. 

10.  Let  them  tell  what  they  know  of  some  of  the  most 
prominent  or  noted  men  of  the  country  or  world. 

11.  Let  them  state  what  they  know  of  the  history  of  the 
town,  township,   county,  state,  country,  or  anything   else 
that  has  a  history.     The  manufacture  of  an  article  from  its 
beginning  to  its  end  or  completion,  may  be  written  in  the 
form  of  a  history.     The  manufacture  of  a  pin,  needle,  knife, 
pen,  pencil,  thimble,  comb,  cent,  bank-note,  hat,  book,  loaf 
of  bread,  pie,  cake,   window-pane,  chair,    table,  sheet  of 
paper,  piece  of  cloth,  etc.,  forms  suitable  subjects  for  this 
purpose. 

12.  Let  them  describe  a  picture,  telling  what  they  see,  or 
imagine  they  see,  in  it,  and  arrange  the  description  in  proper 
order,  so  that  any   one    on   reading  it  or  hearing  it  read 
could  form  a  good  mental  picture  of  it. 

13.  Let  them  write  letters  to  imaginary  friends,  telling 
them  what  they  are  doing,  have  done,  or  expect  to  do  ;  or 
what  they  are  learning  about  an  object,  a  branch  of  study,  a 
town,  county,  state,  country,  man,  an  event  in  history,  etc. 


General  Considerations.  73 

14.  Let  them  say  as  many  things  as  they  can  about  an 
object — a  dog,  cat,  cow,  horse,  pig,  sheep,  table,  chair,  stove, 
door,    window,  clock,  looking-glass,    sofa,    bureau,  bench, 
knife,  tree,  apple,  peach,  pear,  etc.;  and  lead  them  to  see 
that  some  of  the  words  are  the  same  in   all  the  lines  they 
have  written,  and  that  all  can  be  written  in  one  line  by 
using  the  repeated  words  but  once. 

REMARK. — These  exercises  will  enable  the  teacher  to  intro- 
duce punctuation  points  and  connecting  words. 
EXAMPLES  OF  14: 

a.  i.  The  apple  is  large. 

2.  The  apple  is  round. 

3.  The  apple  is  red. 

4.  The  apple  is  ripe. 

5.  The  apple  is  soft. 

Condensed. — The  apple  is  large,  round,  red,  ripe,  and  soil. 

b.  i.  The  apple  is  large. 

2.  The  apple  is  round. 

3.  The  apple  is  ripe. 

4.  The  apple  is  not  soft. 

Condensed. — The  apple   is   large,   round,   and   ripe,   but  not 
soft. 

c.  i.  The  river  is  long. 

2.  The  river  is  wide. 

3.  The  river  is  not  deep. 

Condensed. — The   river   is  long   and   wide,   though   (or  but) 
not  deep. 

d.  i.  The  needle  is  long. 

2.  The  needle  is  thick. 

3.  The  needle  is  not  sharp. 
4.  The  needle  is  not  hard. 

Condensed—  The  needle  is  long  and  thick,  but  neither  sharp 
nor  hard. 

15.  Let  the  pupils  say  (write)  the  same  thing  of  as  many 
objects  as  they  can,  and  then  write  all  in  one  line,  or  sen- 
tence, with  the  repeated  words  used  only  once. 

EXAMPLE  OF  15: 

1.  The  cat  can  run. 

2.  The  dog  can  run. 

3.  The  cow  can  run. 

4.  The  horse  can  run. 

Condensed.— The  cat,  the  dog,  the  cow,  and  the  "horse  can 
run  ;  or  the  cat,  dog,  cow,  and  horse  can  run. 


74  Science  and  Art  of  Education. 

16.  Incorrect  expressions,  such  as  are  frequently  heard 
in  conversation,  may  be  interspersed  among  the  language 
exercises  for  correction — to  teach  the  pupils  the  correct 
expression. 

17.  The  following  expressions  are  frequently  heard,  even 
from  the  lips  of  educated  persons  : 

a.  Go  and  lay  down.     (Lay  down  what  ?) 

b.  He  laid  on  a  sofa  three  weeks.     (Laid  what  on  a  sofa  ?) 

c.  I  lay  down  every  day  an  hour  or  two.    (Lay  down  what  ?) 

d.  He  set  on  a  log  until  noon.     (Set  what  on  a  log?) 

e.  He  lays  in  bed  too  long.     (Lays  what  in  bed  ?) 
/.  He  comes  here  most  every  day.     (Most  day?) 

f.  He  thought  it  was  us.     (Us  was  ?) 
.  It  was  me  who  said  it.     (Me  was  ?) 

/'.  The  river  is  raising.     (Raising  what  ?) 

j.  He  can  do  it  as  good  as  1  can.     (Do  it  good  ?) 

k.  I  know  that  it  was  them.     (Them  was?) 

/.  If  I  was  him  I  would  not  do  it.     (When  ?  Him  was?) 
m.  It  was  her  that  done  it.     (Her  was?   Did  she  done  it?) 

n.  I  wish  that  I  was  a  musician.     (When?) 

o.  This  is  to  be  divided  amongst  you  and  I.     (Amongst  I  ? 

p.  A  person  must  be  stupid  if  they  cannot  do  that.     (A  per- 
son they  ?) 

q.  It  could  not  have  been  her.     (Her  could  not  have  been  ?) 

r.  He  told  me  that  I  can  go.     (How  did  he  know  ?) 

s.  Is  that  him  ?     (Him  is  ?) 

t.  I  expect  you  had  a  good  time  last  night.     (When  do  you 
expect  it?) 

u.  I  wish  that  you  had  went  earlier.     (Why  had  went  ?) 

v.  At  what  hotel  are  you  stopping  at?     (Stopping  what? 
At  stopping  at  ?) 

w.  Who  is  your  letter  from  ?     (From  who  ?) 

x.  Who  are  you  writing  to  ?     (To  who  ?) 

y.  Each  of  the  boys  have  their  books.     (Each  their,  and 
each  have.) 

z.  Leave  me  alone,  I  want  to  sleep.     (Why  alone  you  ?) 

18.  The  various  kinds  of  sentences  (according  to  their 
use)  may  now  gradually  be  introduced.     The   statement 
should  come  first,  next  the  question,  then  the  command, 
and  last  the  exclamation. 

The  statement  is  best  taught  in  comparison  with  expres- 
sions that  are  incomplete,  that  do  not  assert  anything.     For 


General  Considerations.  75 

example  :  Some  of  the  rivers  of  North  America  are  long. 
This  is  a  sentence,  because  it  is  a  complete  statement,  a 
complete  assertion  ;  but,  some  of  the  rivers  of  North  America, 
is  not  a  sentence  ;  it  does  not  state  or  assert  anything ;  it 
is  simply  the  beginning  of  a  statement. 

19.   The  following  exercises  will  furnish  a  large  amount 
of  profitable  language  work  : 

a.  i.  Write  a  request  to  your  teacher  to  permit  you  to 
borrow  a  book  from  one  of  your  classmates. 

2.  Ask  him  to  permit  you  to  go  to  the  library  to  consult 
some  books  of  reference  ;  state  the  information  you  desire, 
and  in  what  books  you  expect  to  find  it. 

3.  Ask  permission  to  leave  school  after  you  have  recited 
your  last  lesson,  giving  a  full  reason  for  your  request. 

4.  Ask  him  to  spend  the  evening  at  your  house,  say  who 
else  has  been  invited,  that  you  expect  a  pleasant  time,  and 
that  your  parents  desire  his  presence. 

5.  Tell  him  how  you  spend  your  evenings  ;  how  much 
time  you  spend  upon  each  lesson,  the  order  in  which  you 
study  your  lessons,  your  methods  of  study,  what  recreations 
you  have,  and  when  you  retire. 

6.  Ask  him  what  the  best  way  is  to  study  each  lesson  ; 
whether  it  makes  any  difference  in  what  order  they  are  pre- 
pared, that  is,  which  comes  first,  which  next,  and  so  on  ; 
and  say  that  you  will  thankfully  receive  any  suggestions 
that  he  may  make  concerning  your  studies. 

b.  i.  Write  to  one  of  your  acquaintances,  asking  what 
school  he  attends,  whether  public  or  private,  what  branches 
he  studies,  which  he  likes  best,  and  how  he  likes  the  school. 

2.  Ask  him  what  profession  or  trade  he  has  in  view,  why 
he  has  selected  it,  which  of  the  branches  he  is  pursuing  will 
be  of  most  service  to  him  in  his  life  work,  and  why. 

3.  Tell  him  that  you  intend  to  spend  next  Saturday  after- 
noon at  fishing,  and  that  you  would  like  to  have  him  ac- 
company you.     Tell  him  what  kind  of  lines  and  hooks  he 


7 6  Science  and  Art  of  Education. 

will  need,  what  kind  of  bait,  where  you  intend  to  go,  and 
where  he  shall  meet  you. 

c.  Ask  one  of  your  classmates  or  acquaintances  to  take  a 
ride  into  the  country  with  you  ;   name  the  objects  of  in- 
terest you  expect  to  see  ;  speak  of  the  enjoyment  his  com- 
pany will  afford  you  ;  state  that  your  father  has  given  his 
consent  for  you  to  go,  and  that  you  will  have  a  good  horse 
and  buggy. 

d.  i.  You  are  visiting  one  of  your  relatives  in  the  coun- 
try.    Write  a  letter  to  your  mother  (if  you  are  a  girl)  telling 
her  of  any  incidents  that  came  under  your  notice  on  your 
way,  at  the  railroad  station  before  starting,  in  the  cars,  or 
after  you  had  left  the  cars.     Tell  her  who  met  you  at  the 
station,  and  how  you  were  received  by  the  family — how 
glad  they  were  to  see  you.     Tell  her,  too,  how  you  spend 
your  time,  whether. you  go  out  into  the  fields,  and  what  you 
see  when  you  do  so. 

2.  Write  to  your  sisters  and  tell  them  how  you  enjoy 
yourself  ;  tell  them  at  what  hours  you  rise  and  retire,  how 
you  spend  your  time  before  breakfast,  what  you  do  after 
breakfast,  how  the  work  of  the  family  is  done,  how  well  it 
is  systematized,  what  is  assigned  to  each  as  a  regular  duty, 
and  how  well  each  performs  his  or  her  part. 

3.  Write  to  your  father  (if  you  are  a  boy)  and  tell  him 
what  you  saw  on  the  way  to  the  station,  how  long  you  had 
to  wait  for  the  cars  and  why,  whom  you  met  at  the  station 
and  what  you  learned  from  them,  whom  you  saw  on  the 
cars,  and  anything  of  interest  that  may  have  occurred  or 
come  under  your  notice  on  the  way. 

4.  Tell   him  the   number  of  cattle  the  people  you  visit 
keep  and  the  kinds,  how  many  horses  they  have,  the  kind 
and  number  of  vehicles,  the  farming  implements  and  where 
they  keep  them,  how  they  do  their  work,  what  crops  they 
raise,  the  condition  of  the  farm  and  buildings,  how  you  are 


General  Considerations.  77 

enjoying  yourself,  and  what  new  things  you  Have  seen  and 
learned. 

e.  A  salesman  is  wanted  in  a  city  clothing  house.     Write 
a  letter  to  the  proprietor  asking  for  particulars  concerning 
the  position  :    i.  Whether  any  other  duties  would  be  re- 
quired but  that  of  being  in  the  store  during  the  day ;  2. 
At  what  hour  in  the  morning  you  would  be   required  to 
begin  work  and  at  what  hour  in  the  evening  close  the  store  ; 
3.  Whether  any  work  would   be   required   in   the  evening 
after  closing  ;   4.  What  salary  may  be  expected. 

Write  a  reply  to  your  letter  as  if  it  came  from  the  pro- 
prietor, giving  definite  information  on  every  point  of  inquiry, 
and  if  the  reply  is  favorable — if  the  position  suits  you,  write 
to  the  proprietor  offering  your  services,  stating  your  ex- 
perience as  a  salesman  and  your  ability  to  win  customers 
and  make  sales.  State,  also,  that,  if  acceptable,  you  are 
willing  to  be  on  trial  a  month  or  more.  It  would  be  of 
service  to  you,  too,  to  state  what  educational  advantages 
you  have  had,  and  that  you  can  bring  testimonials  as  to 
your  moral  character. 

f.  You  have  been  invited  to  an   evening  party  or  enter- 
tainment at  the  house  of  a  friend,  but  find  it  impossible  to 
be    present.     Write    a  letter    expressing   your   regret,    and 
wishing  your  friend  a  pleasant  time. 

g.  Write   the   autobiography   of  a   pin,   ball,   shoe,   nail, 
thimble  ;  piece  of  paper,  cloth,  glass,  bread,  etc. 

h.  You  have  lost  a  valuable  watch.  Write  a  notice  for 
the  paper  describing  the  watch,  telling  where  you  suppose 
you  lost  it,  stating  what  reward  you  will  give  the  finder  on 
delivering  it  to  you,  and  giving  your  place  of  business  or 
residence — street  and  number. 

/.  You  need  an  office-boy  to  run  errands.  Write  an 
advertisement  for  the  paper,  stating  definitely  the  kind  of 
boy  you  want,  what  his  duties  will  be,  and  compensation 
you  will  give. 


78  Science  and  Art  of  Education. 

j.  You  have  received  a  valuable  dog  as  a  present.  Write 
a  letter  to  the  person  from  whom  you  received  it,  thanking 
him  for  it,  and  telling  him  that  you  prize  it  highly,  that  you 
are  fond  of  hunting,  and  this  is  the  kind  of  dog  you  have 
for  some  time  desired  to  get. 

k.  Write  to  a  city  publishing  house  for  the  prices  of 
books  which  you  need,  and  ask  for  the  cheapest  way  of 
sending  them — by  mail  or  by  express. 

/.  Mr.  Hix  wants  to  build.  Write  to  him  and  tell  him 
that  you  will  take  the  contract  at  as  reasonable  a  sum  as 
any  competent  builder  tan  do  it,  and  that  you  will  guarantee 
him  a  good  job.  Give  references  of  persons  for  whom  you 
have  done  similar  work. 

m.  Write  to  a  city  dry-goods  store  for  goods  for  a  spring 
dress,  stating  the  kind  and  quality  you  want,  ask  the  prices, 
and  say  that  if  the  reply  you  receive  is  satisfactory,  you 
would  like  to  know  how  to  send  the  money. 

Write  a  full,  definite  reply,  and  say  that  if  you  intrust 
your  order  to  the  "  house  "  it  shall  receive  prompt  attention 
and  he  in  all  respects  satisfactory. 

Send  the  order,  enclosing  the  money,  and  state  how  the 
goods  shall  be  sent.  After  you  have  received  the  goods, 
acknowledge  the  receipt  of  it,  and  state  how  well  you  are 
pleased  with  your  purchase,  and  that  the  house  may  expect 
further  orders  from  you. 

n.  Samuel  Poll  owes  you  three  hundred  dollars,  and  you 
intend  to  purchase  some  property.  Write  him  a  letter  stat- 
ing that  you  contemplate  making  some  investments,  and 
that  you  should  be  glad  if  he  would  let  you  have  the  money 
by  the  first  of  next  April. 

Write  his  reply.  He  has  been  unfortunate  during  the 
year  ;  the  high  waters  destroyed  his  crops,  carried  away  his 
fences,  and  caused  an  unexpected  outlay  of  money.  Be- 
sides, he  has  lost  one  of  his  best  horses.  He  hopes,  there- 
fore, that  you  will  give  him  more  time. 


General  Considerations.  79 

Since  he  cannot  pay  you  at  the  time  you  named,  he  should 
give  you  an  interest-bearing  note  for  the  money.  Write  the 
note. 

You  need  the  money  and  can  get  it  on  the  note  by  in- 
dorsing it.  Indorse  it  in  full. 

o.  Write  a  receipt  for  payment  in  full  to  date. 

/.  Write  an  order  for  six  different  kinds  of  goods.  Re- 
ceipt it. 

q.  Write  a  note  of  invitation  ;  also  an  acceptance  of  the 
invitation,  stating  the  pleasure  it  will  afford  you  to  spend 
the  afternoon  and  evening  with  the  family  and  their  friends. 

Also  write  a  note  expressing  your  inability  to  accept  the 
invitation,  owing  to  sickness  in  your  family,  and  express 
the  desire  that  the  family  shall  pay  you  a  visit. 

r.  Write  a  due-bill,  and  state  how  the  debt  is  to  be  dis- 
charged, whether  with  money  or  with  goods.  If  with  goods, 
name  the  kinds  and  quality. 

s.  Write  a  notice  of  meeting  to  be  held,  naming  the  place, 
the  object,  the  day,  and  the  hour. 

/.  Write  an  advertisement  for  the  sale  of  household  goods, 
stating  the  place,  the  day  and  hour,  the  articles  to  be 
offered  for  sale,  and  the  conditions  upon  which  they  are  to 
be  sold. 

For  an  additional  number  of  good  topics  for  Language 
and  Composition,  see  Our  Language,  published  by  Leach, 
Shewell  &  Sanborn,  87  Franklin  Street,  Boston  ;  Studies 
in  English  Composition,  published  by  Allyn  &  Bacon, 
Boston  ;  Shaw's  English  Composition,  published  by  Henry 
Holt  &  Co.,  29  West  Twenty-third  Street,  New  York. 

20.  The  classes  of  words  (parts  of  speech),  of  which  the 
English  language  is  composed,  as  has  already  been  stated, 
should  be  taught  in  connection  with  reading  and  language 
exercises,  and  may  be  commenced  in  the  Second  Reader. 

The  simplest  name  should  be  applied  to  each  class  of 
words,  a  name,  as  far  as  possible,  to  which  the  children  can 


8o  Science- and  Art  of  Education. 

attach  the  proper  meaning.  The  noun,  for  example,  may 
be  called  the  name-word  ;  the  verb,  the  telling-word ; 
the  adjective,  the  kind-word  ;  the  preposition,  the  relation- 
word  ;  the  adverb,  the  how,  when,  and  where  word  (as  the 
case  may  be)  ;  the  conjunction,  the  connecting-word  ;  and 
so  on. 

21.  The  classification  of    sentences    according  to    form 
into  simple,  complex,  and  compound,  may  gradually  be  in- 
troduced. 

22.  The  various  forms  of  phrases  should  be  taught  in 
connection  with  simple  sentences,  and  those  of  clauses  with 
complex.     At  the   same  time   it   may  also   be  shown  that 
phrases  and  clauses  are  substitutes  for  words,  and  enable  us 
to  give  not  only  variety  to  our  expressions,  but  frequently 
greater  clearness. 

23.  A  knowledge  of    the    different  forms    of  sentences, 
phrases,  and  clauses  is  best  acquired  by  practice  in  writing 
them,  substituting  one  form  for  another,  and  pointing  out 
and  discussing  their  various  elements,  relations,  and  uses. 

REMARK. — As  soon  as  the  pupils  can  readily  recognize  the 
simpler  grammatical  distinctions,  they  may  with  some  advan- 
tage begin  to  use  a  book  on  grammar  for  reference. 

24.  Substitute   equivalent    phrases    for    the    underlined 
words  in  the  following  exercises  : 

a.  He  passed  my  sister's  house. 

b.  She  waited  anxiously  for  the  doctor. 

c.  I  could  not  hear  him  for  the  noise. 

d.  The  directors  meet  monthly. 

e.  He  occupies  an  influential  position. 

f.  They  had  erected  a  brazen  image. 

g.  Hence  you  will  see  the  necessity  of  it. 
h.  American  ideas  are  liberal. 

*.  The  old  oaken  bucket  had  fallen  to  pieces 
j.  The  doctor  is  an  intelligent  man. 

25.  For  the  phrases  in  the  following  sentences  substitute 
equivalent  clauses  : 


General  Considerations.  8 1 

a.  The  wool  of  the  sheep  affords  us  clothing. 

b.  None  in  the  village  suspected  him  of  the  deed. 

c.  With  diligence  he  must  succeed. 

d.  I  will  show  you  the  place  of  my  birth. 

f.  No  one  of  my  acquaintance  was  in  the  room. 
/.  I  will  tell  you  the  reason  of  my  acting  so. 

g.  Do  you  know  the  age  of  the  child  ? 

26.  Change  the  clauses   in    the  following  sentences   to 
equivalent  phrases  : 

a.  I  see  no  way  in  which  I  can  improve  it. 

b.  Any  person  who  has  good  manners  will  be  received. 

c.  His  house  stands  where  the  battle  was  fought. 

d.  All  stood  with  uncovered  heads  while  he  read  the  service. 

e.  When  they  heard  the  news  they  jumped  for  joy. 

27.  For  the  phrases  in  the  following  sentences  substitute 
words  of  equivalent  meaning  : 

a.  He  found  it  of  benefit  to  use. 

b.  She  calls  upon  them  every  day. 

c.  He  selected  it  in  place  of  his  brother.    ' 

d.  Your  conduct  was  like  that  of  a  tyrant. 

e.  It  would  be  of  no  use  to  try  again. 

/.  They  did  it  without  the  authority  of  law. 

28.  Make  a  simple  sentence  of  each  set  of  the  following 
elements  : 

a.  In  America  the  railways  are  frequently  single  lines.     The 
railways  are  formed  to  carry  a  limited  commerce.     Sidings  are 
provided  at  convenient  situations. 

b.  The  river  overflowed.     The  river  was  the  Ohio.     This  w;>s 
in  January.     It  happened  on  the  tenth  of  the  month. 

c.  Wodin   was  the  chief  god  of  the  Old    English   people. 
Wodin  was  by  the  Danes  called  Odin.     He  was  the  chief  giver 
of  valor.     He  was  the  chief  giver  of  victory. 

d.  John  Wycliffe  did  a  great  work.     This  great  work  was  a 
translation  of  the  Bible.     The  translation  was  made  by  himself. 
He  was  assisted  by  several  friends  and  followers. 

e.  The  English  fearlessly  boarded  the  ships.     The  ships  were 
those  of  the  enemy.     They  cut  the  rigging.     They  gained  the 
victory.     The  victory  was  easily  won. 

/.  The  next  morning  the  battle  began  in  terrible  earnest. 
The  next  morning  was  the  24th  of  June.  The  battle  began  at 
break  of  day. 

g.  Columbus  returned  to  Spain  in  1493.     He  had  spent  some 


82  Science  and  Art  of  Education. 

months  in  exploring  the  delightful  regions.  These  regions  had 
long  been  dreamed  of  by  many.  These  regions  were  now  first 
thrown  open  to  European  eyes.  Columbus  had  been  absent 
seven  months  and  eleven  days. 

29.  Combine  each  of  the  following  sets  of  simple  sen- 
tences into  a  complex  sentence. 

a.  Tin  is  a  metal.     Ancient  Britain  was  most  famous  for  tin. 
The  Phoenicians  were  first  induced  to  visit  Britain  for  tin. 

b.  He  spoke  to  the  king  like  a  rough  man.     I  think  this  my- 
self.    He  was  a  rough  angry  man.     He  did  nothing  more. 

c.  The  ingenuity  of  man  has  made  a  lever  of  the  mind.     This 
lever  spares  him  an  immensity  of  toil.     This  lever  is  applied  to 
machinery. 

d.  The   ships  of   Sesostris,  the   Egyptian   conqueror,   were 
formed   of  cedar.     One  of  these  ships  was   280  cubits   long. 
Ancient  writers  notice  this.     The  gigantic  statue  of  Diana  in 
the  temple  of  Ephesus  was  also  formed  of  this  timber. 

e.  Andrew  Douglas  was  willing  to  share  the  danger  and  the 
honor.     Andrew  Douglas  was  master  of  the  Phcenix.     He  had 
on  board  a  great  quantity  of  meal  from  Scotland. 

/.  Three  or  four  bounds  of  the  horse  carried  us  out  of  reach 
of  the  enemy.  The  enemy  quickly  resumed  his  flight.  The 
enemy  had  merely  turned  in  desperate  self-defence. 

g.  God  in  his  good  has  covered  the  earth  with  herbs  and 
trees.  We  inhabit  the  earth.  These  herbs  and  trees  furnish 
us  with  food,  clothing,  and  other  articles.  These  articles  con- 
tribute to  our  comfort  and  luxury. 

h.  At  length  the  mystery  of  the  ocean  was  revealed.  The 
theory  of  the  great  navigator  was  triumphantly  established. 
The  theory  had  been  the  scoff  of  sages.  He  had  secured  to 
himself  glory,  This  glory  must  be  durable.  The  world  itself 
is  durable. 

30.  Change  the  following  simple  sentences  to  compound 
sentences  : 

a.  The   Rhone,  flowing  into  the  Lake  of  Geneva,  emerged 
from  it  at  the  town  of  the  same  name. 

b.  These  events,  trifling  doubtless  in  the  estimation  of  the 
reader,  were  affecting  to  me  in  the  highest  degree. 

c.  Snatching  the  handkerchief,  he  quickly  wrapped  it  around 
the  wounded  part. 

d.  The  trees  met  overhead,  forming  an  archway. 

e.  On  further  consideration  I  have  decided  to  remain. 

/.  After  a  moment's  reflection  he  proceeded  to  pass  sentence. 
g.  The  king,  a  man  of  rare  vigor,  would  allow  no  foreign 
prince  to  encroach  on  his  rights. 


General  Considerations.  83 

//.  In  forwarding  your  own  interests,  do  not  impede  those  of 
others. 

/".  The  coral  insect,  barely  possessing  life,  is  hourly  creating 
habitations  for  men. 

31.  Combine  each  set  of  the  following  simple  sentences 
into  a  compound  sentence  : 

a.  They  next  erected  a  crucifix.     They  prostrated  themselves 
before  it.     They  returned  thanks  to  God.     God  had  conducted 
their  voyage  to  such  a  happy  issue. 

b.  He  possessed  quick  perceptions.     He  observed  accurate- 
ly.    He  was  able  to  place  his  hand  on  the  right  animals.     He 
did  so  without  hesitation. 

c.  The  island  at  first  seemed  uninhabited.     The  natives  grad- 
ually assembled  in  groups  upon  the  shore.     The  natives  grad- 
ually overcame  their  natural  shyness.     The  natives  received  us 
very  hospitably.     They  brought  down  for  our  use  the  various 
products  of  their  island. 

d.  The  struggle  was  now  at  an  end.     The  inhabitants  were 
terror-stricken.     They  burst  through  the  lines.     They  fled  in 
every  direction. 

e.  They  saw   their  leader  fall.     They  thought  him    slain. 
They  at  once  gave  up  the  contest.     This  was  in  accordance 
with  the  practice  of  their  ancestors. 

/.  Steam  has  increased  indefinitely  the  mass  of  human  com- 
forts. Steam  has  increased  indefinitely  the  mass  of  human  en- 
joyments. Steam  has  rendered  cheap  the  materials  of  wealth 
and  prosperity.  Steam  has  rendered  accessible  the  materials 
of  wealth  and  prosperity.  It  has  done  so  all  over  the  world. 

g.  The  sun  then  broke  out.  The  sun  dispersed  the  vapor 
and  the  cold  with  his  welcome  beams.  The  traveller  felt  the 
general  warmth.  The  sun  shone  brighter  and  brighter.  The 
traveller  sat  down.  The  traveller  was  overpowered  by  the 
heat.  The  traveller  cast  his  cloak  upon  the  ground. 

32.  Change  the  following  compound  sentences  to  com- 
plex sentences: 

a.  You  have  asked  me  a  question  and  I  have  answered  it. 

b.  The  statement  is  false  and  he  knows  it. 

c.  They  did  not  know  their  lesson  and  so  he  kept  them  in. 

d.  Finish  this  and  then  I  will  let  you  go. 

e.  He  was  very  ill,  but  still  he  tried  to  finish  it. 
/.  A  boy  had  seen  it  fall  and  had  picked  it  up. 

g.  He  tried  several  keys,  but  none  of  them  would  fit  it. 

For  a  greater  variety  of  exercises  in  the  various  kinds  of 
sentences,  see  First  Steps  and  Second  Steps  in  English 


84  Science  and  Art  of  Education. 

Composition,  published  by  W.  Stewart  &  Co.,  London, 
England  ;  Practical  Exercises  in  Composition,  and  Exer- 
cises in  English,  by  H.  I.  Strang,  the  former  published  by 
The  Educational  Publishing  Co.,  Boston,  the  latter  by  D. 
C.  Heath  &  Co.,  Boston.  Kerl's  Composition  and  Rhet- 
oric is  also  a  good  book  for  sentence  and  composition 
work  ;  published  by  American  Book  Co.,  New  York. 

33.  Exercises    in   the   discrimination    of   words   should 
form  part  of  the  sentence  work. 

Write  sentences  in  which  the  following  words  shall  be  cor- 
rectly used :  Raise,  rise ;  sit,  set ;  bring,  fetch  ;  fly,  flee ;  flow, 
flew,  fled ;  shut,  close ;  board,  feed ;  hung,  hanged  ;  lay,  lie ; 
leave,  let ;  lend,  borrow;  lose,  loose  ;  teach,  learn  ;.  wring,  ring; 
begin,  commence;  forsake,  desert;  load,  burden;  empty,  va- 
cant ;' sleigh,  slay ;  expect,  suspect,  suppose ;  believe,  calculate ; 
may,  can ;  fix,  repair,  mend ;  think,  guess ;  enjoy,  possess ;  be- 
tween, among;  invent,  discover ;  handsful,  handfuls;  preacher, 
minister,  pastor,  clergyman  ;  sow,  sew ;  luck,  success ;  station- 
ary, stationery ;  desert,  dessert ;  continual,  continued  ;  compo- 
sition, essay ;  there,  their;  hard,  difficult;  balance,  remainder; 
advice,  advrse ;  all,  awl ;  aloud,  allowed  ;  altar,  alter ;  ant,  aunt ; 
ascent,  assent;  assistance,  assistants;  bail,  bale;  bait,  bate; 
bald,  bawld ;  bear,  bare ;  base,  bass ;  beat,  beet ;  blew,  blue ; 
bawl,  ball ;  burrow,  borough  ;  bough,  bow ;  cannon,  canon  ; 
capital,  capitol ;  ceiling,  sealing;  cell,  sell;  cent,  sent,  scent; 
chord,  cord ;  site,  cite,  sight ;  climb,  clime ;  council,  counsel ; 
fare,  fair;  gait,  gate;  great,  grate;  holy,  wholly ;  gage,  gauge; 
hail,  hale;  pale,  pail;  pane,  pain;  plane,  plain;  pray,  prey; 
rain,  rein,  reign  ;  sale,  sail ;  strait,  straight ;  vane,  vain,  vein  ; 
pare,  pear,  pair ;  canvass,  canvas  ;  tacks,  tax  ;  claws,  clause  ; 
nought,  naught ;  feet,  feat,  leave,  lieve ;  meet,  mete,  meat ; 
peel,  peal;  pleas,  please;  seed,  cede;  seas,  sees,  seize;  heard, 
herd;  lesson,  lessen  ;  miner,  minor;  petition,  partition  ;  of,  off. 

34.  The   properties   that  characterize  well-written   sen- 
tences, paragraphs,  and  essays,  under   the  usual  titles  of 
purity,  propriety,  precision,  and  clearness,  strength,  unity, 
and  harmony,  should  not,  as  is  usual,  be  postponed  until  a 
late  period  of  a  pupil's  school  life,  but  should  as  early  as  is 
possible  be  introduced  by  directing  his  attention  to  merito- 
rious as  well  as  to  faulty  constructions,  and  demanding  cor- 


[UNIVERSITY 

General  Considera 


rections  or  improvements  so  far  as  he  is  capable  of  seeing 
their  force  and  making  them. 

35.  The  only  sure  way  of  training  pupils  to  the  careful 
use  of  English  is  to  begin  as  early  as  their  years  permit,  and 
to  demand  that  every  exercise  of  theirs  shall  be  as  nearly 
perfect  as  they  can  make  it  ;  and  this  course  must  be  con- 
tinued to  the  end  of  their  school  days. 

36.  Essays.  —  When  pupils  have  acquired  sufficient  power 
of  thought  and  skill  in  expression  to  write  essays,  subjects 
for  the  purpose  may  be  assigned  them.     Care  must,  however, 
be  taken  that  no  abstract  subjects,  no  subjects  beyond  their 
comprehension,  nor  anything  in  which  they  cannot  be  inter- 
ested, be  given. 

37.  After  a  general  subject  has  been  selected  or  assigned, 
it  should  be  considered  in  all  its  bearings,  and  some  special 
line  of  thought  or  view  of  it  decided  upon. 

REMARK.  —  Writing  upon  general  subjects  cannot  end  in  any- 
thing definite. 

38.  Having  determined  upon  the  line  of  discussion,  the 
next  thing  is  to  keep  it  before  the  mind  until  it  has  been 
thoroughly  thought  over  and  everything  found  that  has  a 
direct  bearing  upon  it.     This  done,  a  careful,  logical  out- 
line of  the  main  and  sub-topics  should  be  made,  containing 
nothing  not  strictly  in  accord  with  the  determined  line  of 
thought. 

REMARK.  —  Finding  the  matter  for  the  essay  and  making  the 
outline  constitute  the  most  important  and  difficult  part  of  the 
work. 

39.  Next  comes  the  writing,  the  composition.     A  good 
plan  to  pursue  is,  to  write  a  little  essay,  as  it  were,  upon 
each  main  topic,  combine  them  into  one,  look  it  ovec  to 
correct  errors,  then  lay  it  away  for  a  few  days  or  a  week 
before  re-examination  and  rewriting.     An  essay  should  be 
several  times  carefully  examined  and  rewritten  before  it  is 
handed  to  the  teacher  for  inspection  and  suggestions. 


86  Science  and  Art  of  Education. 

40.  Unless   intended   for  a   public   audience,   no   essay 
handed  to  the  teacher  should  be  corrected  by  him  ;  only  the 
place  where  an  error  exists  should  be  indicated  by  some 
general  mark  or  sign,  and  the  pupil,  at  least  at  first,  left  to 
discover  the  fault  himself.     It  is  only  by  practice  in  discov- 
ering that  discovering  is  learned. 

41.  An  essay  should  be  handed  two,  three,  or  more  times 
to  the  teacher  for  inspection  and  criticism,  and  as  many 
times  rewritten.     In  short,  it  should  be  criticised  and  re- 
written until  it  is  free  from  errors. 

In  few  things,  if  in  any,  do  we  find  more  failures  in 
teaching  than  in  composition,  and  the  best  book  on  essay 
writing  is  a  competent  teacher. 

The  following  books  on  composition,  in  addition  to  those 
already  named,  may  be  used  with  advantage  by  teachers  : 
Longmans'  School  Composition,  published  by  Longmans, 
Green  &  Co.,  New  York  ;  The  Foundations  of  Rhetoric, 
published  by  Harper  &  Brothers,  New  York  ;  Composition 
and  Practical  English,  by  William  Williams,  published  by 
D.  C.  Heath  &  Co.,  Boston.  For  lower  grades  of  schools, 
the  following  will  prove  serviceable  :  Stories  for  Composi- 
tion, published  by  Educational  Publishing  Co.,  Boston  ; 
How  to  Write  a  Composition,  published  by  Dick  &  Fitzger- 
ald, New  York  ;  Primary  Reproduction  Stories,  and  Hall's 
Composition  Outlines,  published  by  A.  Flanagan  &  Co., 
Chicago  ;  The  Writing  of  Compositions,  published  by  E. 
L.  Kellogg  &  Co.,  New  York  ;  and  W.  B.  Powell's  whole 
series  of  language  books,  published  by  E.  H.  Butler  &  Co., 
Philadelphia. 

Nearly  all  the  foregoing  books  can  be  had  of  E.  L.  Kel- 
logg &  Co.,  6 1  East  Ninth  Street,  New  York. 


SUGGESTIONS   FOR  TEACHING 
NUMBERS. 

TEACH  the  concept  (idea)  concretely,  with  pebbles,  beans, 
grains  of  corn,  shoe-pegs  (colored  or  plain),  spools,  squares, 
cubes,  balls  (spheres),  cylinders,  triangles  ;  in  short,  with 
any  suitable  objects  that  may  be  had.  A  variety  of  objects 
should  be  kept  on  hand  for  this  purpose. 

Figures  should  not  be  introduced  until  the  children  can 
work  well  with  objects,  pictures,  etc.,  and  until  they  will 
not  confound  figures  with  numbers. 

Color  and  form  should  be  taught  in  connection  with 
numbers. 

LESSON  ON  Two. 
a.    What  the  Pupils  must  Discover. 

1.  i  -|-  i  =  5.  2  —  2  =  9.  f  of  i  = 

2.  I    X   2  =  6.    2  -I-  I  =  10.    \  Of  2  = 

3.  2   X    I  =  7-     2  -r-  2  =  II.    f  Of  2  = 

4.  2  —  I  =  8.    i  Of  I  =  12.    f   = 

b.  For  seat  work  trje  following  notation  may  be  used  with 
children  that  are  not  far  enough  advanced  to  write  words 
or  to  use  figures  : 


I. 

i  +  i 

=  11 

5- 

ii 

—  ii 

= 

o 

9- 

f(i  ) 

=1  = 

2. 

1X1: 

t  =  n 

6. 

1  1 

-^i 

= 

II 

10. 

i(») 

=1  + 

3- 

11X1 

=  11 

7- 

ii 

-T-II 

= 

I 

ii. 

f  (n) 

=f  + 

4- 

ii  —  i 

=  i 

8. 

i 

(i) 

= 

i 

12. 

f 

=i 

NOTE.—  i.  The  teacher  should  substitute  some  form  of  the 
concrete  for  the  fractions  in  the  seat-work,  until  the  children 
can  use  figures.  A  short  vertical  line  divided  into  two  equal 

87 


Science  and  Art  of  Education. 


parts,  with  a  nought  covering  the  upper  part,  might  represent 
\;  both  parts  uncovered,  f ;  the  line  divided  into  three  equal 
parts,  with  the  upper  part  covered,  % ;  with  the  two  upper  parts 
covered,  £,  etc. 

2.  Horizontal  lines,  squares,  triangles,  circles,  and  pictures  of 
suitable  objects  may  be  used  by  the  children  in  performing  the 
fractional  work ;  the  whole  object  or  picture   representing  or 
being  the  unit,  and  the  parts  the  fractions. 

3.  In  solving  problems  in  which  a  fractional  part  is  required 
of  a  number  consisting  of  several  ones,  or  units,  the  children 
should  first  be  taught  to  find  the  sum  of  the  fractional  parts 
of  the   separate  units;   later,  after  they  can   readily  do  this, 
they  should  be  taught  the  usual  way  of  obtaining  the  result. 
Problem  10  of  the  foregoing  seat-work  may  be  solved  with  two 
horizontal  lines,  one  of  the  halves  of  each  being  covered  with  a 
nought  or  some  other  device  to  indicate  that  it  is  not  to  be 
counted.    It  may  also  be  solved  with  squares,  as  follows : 

n+mmn. 

c.  Suggestive  Questions  and  Problems. 

1.  Give  me  a  cube.     Give  me  another.     How  many  have 
I  now  ?    (One  and  one  are  called  two;  or,  simply,  are  two.) 

2.  Show  me  two  fingers,  two  hands,  two  boys,  a  two  of 
red  cubes,  a  two  of  pencils,  a  two  of  anything  else. 

REMARK.— A  two  of  anything  means  two  things  taken  to- 
gether and  considered  as  a  unit. 

3.  One  bird  and  one  bird  are  how  many  birds  ? 

4.  Show  me  a  two.     Show  me  a  one.     How  many  ones 
are  in  a  two  ? 

5.  If  two  birds  are  on  a  tree  and  one  of  them  flies  away, 
how  many  remain  ? 

6.  What  number  is  one  more  than  one  ? 

7.  What  number  is  one  less  than  two  ? 

REMARK. — Every  operation  should  be  proved  or  illustrated 
with  objects  or  drawings  of  them. 

8.  How  many  twos  are  in  two  ones  ?     How  many  ones 
does  it  take  to  make  a  two  ? 

9.  From  a  two  take  away  two  ones,  and  what  have  you 
left.?     Prove  it  with  yellow  cubes. 


Suggestions  for  Teaching  Numbers. 


10.  From  two  ones  take  away  a  two,  and  what  have  you 
left  ?  Prove  it  with  blue  cylinders. 

d.  Suggestive  Dialogue  to  Teach  the  Half. 

Teacher.  If  you  wanted  to  give  me  half  of  an  apple,  how 
would  you  cut  (or  divide)  the  apple  ? 

Pupil,  I  would  cut  it  through  the  middle. 

T.  Which  one  of  us  would  get  the  larger  piece  ? 

P.  Neither;  one  piece  would  be  as  large  as  the  other. 

T.  Make  a  picture-apple  upon  the  blackboard,  and  draw 
a  line  through  it  where  you  would  cut  it. 

T.  Here  are  two  pieces  of  cardboard;  which  of  them  is 
the  longer  ? 

P.  One  is  as  long  as  the  other. 

T.  How  much  longer  are  the  two  pieces  together  than 
this  piece  ? 

P.  They  are  just  as  long. 

T.  If  I  should  cut  the  long  piece  across  the  middle,  which 
of  the  two  parts  would  be  the  longer  ? 

P.  Neither  piece  would  be  longer  than  the  other. 

T.  What  part  of  the  whole  piece  would  each  of  the 
parts  be  ? 

P.  One  half. 

T.  What  did  I  do  ? 

P.  You  cut  the  long  piece  through  the  middle. 

T.  How  can  you  tell  that  I  cut  it  through  the  middle  ? 

P.  By  trying  whether  one  piece  is  as  long  as  the  other. 

T.  You  may  try  it. 

P.  One  piece  is  just  as  long  as  the  other. 

T.  What  part  of  the  whole  piece  do  I  hold  in  my  hand  ? 

P.  One  half. 

T.  One  half  of  what  ? 

P.  Of  the  whole  piece. 

T.  Lay  one  piece  at  the  end  of  the  other,  and  see  what 
the  two  halves  make. 


Science  and  Art  of  Education, 


P.  They  make  the  whole  piece. 

T.  Since  these  two  pieces  make  the  whole  piece,  one 
vi  them  is  what  part  of  two  ? 

P.  One  half. 

T.  How  do  you  know  that  each  piece  is  one  half  of  the 
two  pieces  ? 

P.  Because  it  is  one  half  of  the  whole  piece,  and  the 
whole  is  made  of  the  two  pieces. 

T.  Which  of  these  two  yellow  cubes  is  the  larger  ? 

P.  One  is  as  large  as  the  other. 

T.  How  do  you  know  ? 

P.  I  have  tried  them. 

T.  Now  since  one  of  the  two  pieces  of  cardboard  is  one 
half  of  the  two  pieces,  what  part  do  you  think  one  cube  is 
of  the  two  cubes  ? 

P.  One  half. 

T.  One  apple  is  what  part  of  two  apples  ? 

P.  If  they  are  of  the  same  size,  it  is  one  half  of  them. 

T.  How  many  halves  are  in  the  whole  of  anything  ? 

P.  Two. 

T.  How  can  I  get  one  half  of  anything  —  of  an  orange, 
for  example  ? 

P.  By  cutting  it  through  the  middle. 

T.  Why  .cut  it  through  the  middle  ? 

P.  To  make  one  piece  as  large  as  the  other. 

T.  Why  must  one  piece  be  as  large  as  the  other  r 

P.  If  they  were  not  of  the  same  size  they  would  not  be 
halves. 

T.  How  can  I  get  one  half  of  two  candies  ? 

P.  By  breaking  each  one  into  two  equal  pieces,  and  tak- 
ing a  piece  of  each  of  them. 

T.  Cculd  you  get  a  half  of  the  two  in  any  other  way  ? 

P.  If  one  of  the  candies  is  as  large  as  the  other,  one  of 
them  would  be  a  half  of  the  two. 

T.  Which  one  of  them  ? 


Suggestions  for  Teaching  Numbers.  91 

P.  Either  one. 

T.  How  can  you  tell  ? 

P.  Because  one  is  as  large  as  the  other. 

T.  Are  all  halves  of  the  same  size  ? 

P.  Yes,  they  are. 

T.  You  may  draw  two  picture-apples  upon  the  black- 
board, making  one  larger  than  the  other. 

T.  Draw  a  line  through  the  middle  of  each,  and  then  tell 
me  whether  the  halves  of  the  small  one  are  as  large  as  those 
of  the  large  one. 

P.  No;  they  are  not. 

T.  Do  you  still  think  that  all  halves  are  of  the  same  size  ? 

P.  No;  I  do  not. 

T.  What  halves,  then,  are  of  the  same  size  ? 

P.  Those  of  the  same  thing,  or  of  things  of  the  same  size. 

T.  In  how  many  ways  could  you  cut  this  card  (parallel- 
ogram, i  in.  by  2  in.)  into  halves  ? 

T.  I  will  give  you  a  card  and  you  may  draw  a  pencil- 
mark  across  where  you  would  cut  it,  and  then  tell  me  in 
how  many  ways  you  could  cut  it  ? 

P.  I  could  cut  it  in  two  ways,  lengthwise  and  crosswise. 

T.  I  will  give  you  another  card,  and  you  may  cut  one  of 
them  lengthwise  and  the  other  crosswise,  and  then  tell  me 
whether  all  the  halves  are  of  the  same  size  ? 

P.  No,  they  are  not  ;  the  pieces  of  the  card  cut  length- 
wise are  longer  than  those  of  the  one  cut  crosswise. 

T.  Do  you  notice  any  other  difference  ? 

P.  Yes,  the  short  pieces  are  broader  than  the  others 

T.  Find  out  how  much  broader  they  are  ? 

P.  They  are  twice  as  broad. 

T.  Now  cut  one  of  the  short  pieces  into  two  equal  pieces 
and  see  whether  the  two  parts  laid  together  make  a  piece 
as  long  as  one  of  the  long  pieces. 

P.  Yes,  they  do. 

T.  What  can  you  again  say  of  the  halves  of  anything  ? 


92  Science  and  Art  of  Education. 

P.  That  one  is  as  large  as  the  other. 

T.  In  how  many  ways  did  you  cut  your  card  into  halves  ? 

P.  In  two  ways. 

T.  What  are  they  ? 

P.  Lengthwise  and  crosswise. 

T.  Can  you  cut  them  in  any  other  way  so  that  the  two 
parts  will  be  of  the  same  size  ? 

P.  I  think  I  can,  but  I  am  not  sure  of  it. 

T.  You  may  try  it. 

P.  Yes,  I  can  cut  them  in  another  way — I  can  cut  them 
from  one  corner  across  the  middle  to  the  opposite  corner. 

T.  How  do  you  know  that  the  pieces  are  of  the  same 
size  ? 

P.  I  laid  one  upon  the  other  and  it  covered  it  exactly. 

T.  Show  me  half  of  your  cubes. 

T.  Of  how  many  do  you  show  me  a  half  ? 

P.  Of  two. 

T.  How  many  halves  does  it  take  to  make  the  whole  of 
anything  ? 

P.  Two. 

T.  Two  what  ? 

P.  Two  halves. 

T.  To  make  what  ? 

P.  To  make  the  whole  of  anything. 

e.  Suggestive  Dialogue   to  Teach  the  Applications  in    Two. 

T,  What  do  I  hold  in  my  hand  ? 
P.  A  two-cent  piece. 

T.  How  many  cents  would  you  give  me  for  it  ? 
P.  Two. 

T.  How  many  cent-candies  could  you  get  for  one  cent  ? 
P.  One. 

T.  Illustrate  (show)  it  with  pictures  upon  the  black- 
ooard  ;  also  with  toy-money  and  crayons. 


Suggestions  for  Teaching  Numbers.  93 

T.  How  many  cent-apples  could  you  get  for  two  cents  ? 

P.  Two. 

T.  Prove  (show,  illustrate)  it  with  picture-apples  and 
picture-cents. 

T.  If  I  should  send  you  to  the  store  to  buy  two  slate- 
pencils  that  cost  a  cent  each,  how  much  money  would  you 
pay  for  them  ? 

P.  Two  cents. 

T.  Your  sister  sends  you  to  the  store  with  a  two-cent 
piece  to  buy  an  orange  that  costs  a  cent;  how  much  money 
will  you  bring  back  ? 

P.  One  cent. 

T.  If  you  should  go  to  the  post-office  with  two  cents  to 
buy  cent-stamps,  how  many  would  you  get  ? 

P.  Two. 

T.  Henry  has  two  rabbits,  and  this  is  one  more  than 
Sarah  has  ;  How  many  has  Sarah  ? 

P.  One. 

T.  John  has  half  as  many  roses  as  his  sister  ;  if  he  has 
one,  how  many  has  she  ? 

P.  Two. 

T.  I  know  a  number  whose  double  is  two,  what  is  it  ? 

P.  One. 

T.  What  number  is  that  whose  half  is  one  ? 

P.  Two. 

LESSON  ON  THREE. 
a.    What  the  Pupils  must  Discover. 

1.  2 -f  i  =  8.  3-*- 3  =  15.  f  of  2  = 

2.  I  +  2  =  9-    3  -f-   I   =  l6.    f  Of    2  = 

3.  i  X  3  =  10.  3  -s-  2  =  17.  \  of  3  = 

4.  3  X  i  =  ii.  i  of  i  —  18.  f  of  3  - 

5.  3  —  i  =  12.  f  of  i  =  19.  £  of  3  — 

6.  3  -  2  =  13.  |  of  i  =  20.  f  of  3  = 

7.  3  —  3  -  14.  \  of  2  =  21.  |  of  3  = 


94  Science  and  Art  of  Education. 

REMARK.  —  i.  In  3  -s-  2,  the  question  is,  how  many  twos  are 
in  three  ;  and  the  answer  is,  one  two  and  one  one,  and  may  be 
written  thus,  i  (i),  the  parenthetic  part  being  the  remainder. 

2.  The  yard  with  its  parts  in  feet  should  be  taught  in  connec- 
tion with  the  foregoing. 

b.  For  seat-work  the  following  will  serve  as  example  : 

1.  11  +  1   =IH  4.  in  xi  =  11  1  7.  m  —  iii=o 

2.  I     -f  II=III  5.    Ill    —1=    II  8.    III-i~III  =  I 

3.  i  xn  1  =  1  1  1  6.  in  —  1  1  =  1  9.  iii-7-i  =  in 
10.111  -5-    ii  =  i(i)                             16.  i(n)  =1+1  =  11 

11.  i  (i)  =i  17- 

12.  |(i)   =f  18. 

13-  1(0  =l=i  19-  i("i)=i+t+i=t= 

14.  i  (")=*+*=!  20.  f  (in)=£  +  |+|=ii 

15-   I  (")=f  +1=1*  21.    |  (Ill)=f  +  f  +  f  =  HI 


NOTE.  —  The  method  of  solution  is  indicated  in  all  the  exer- 
cises that  follow  the  tenth. 

REMARK.  —  i.  As  before  remarked,  instead  of  the  foregoing 
notation,  horizontal  lines,  squares,  triangles,  circles,  and  pict- 
ures may  be  used  for  performing  all  the  fractional  work.  For 
examples,  the  2oth  of  the  foregoing  may  be  solved  thus,  with 
squares  : 

nitiMMD-iiD  n  a 

REMARK.  —  2.  The  pupils  should  be  required  to  make  stories 
of  their  exercises.  Of  No.  i  of  the  foregoing  the  following 
may  be  made  :  I  had  two  cents  and  my  sister  gave  me  another; 
then  I  had  three.  Or,  Sarah  had  two  roses  and  her  mother 
gave  her  another  ;  how  many  had  she  then  ? 

c.  Suggestive  Questions  and  Problems. 

1.  Give  me  two  red  spheres  (balls).     Give  me  another. 
How  many  have  you  given  me  altogether?     (Two  and  one 
are  three). 

2.  Show  me   three   fingers,  three  cylinders,  three  girls, 
three  boys. 

3.  What  number  is  one  more  than  two  ? 

4.  Three  i$  one  more  than  what  number  ? 


Suggestions  for  Teaching  Numbers.  95 

5.  One  is  two  less  than  what  number  ? 

6.  What  number  is  less  than  three  ? 

7.  What  number  is  two  more  than  one  ? 

8.  To  what    number   must    I   put    (add)    one   to  make 
three  ? 

9.  One  and  one  and  one  are  how  many  ones  ? 

10.  Show  me  a  two,  also  two  ones  ;  which  is  the  larger? 

1 1.  How  many  ones  are  in  a  two  ?     In  a  three  ? 

12.  How  many  twos  are  in  a  three,  or  in  three  ones? 

13.  Make  three  in  all  the  ways  you  can. 

14.  Make  three  picture-boys  on  your  tablet,  three  pict- 
ure-girls,  three  picture-horses,  three  picture-wagons,  three 
picture-cats. 

15.  Under  each  of  three  trees  John  found  an  apple;  how 
many  apples  did  he  find  ? 

1 6.  Three  mice  were  in  a  box  and  Charles  killed  all  but 
two  ;  how  many  did  he  kill  ? 

17.  Henry  had  three  roses  and  gave  all  but  one  to  Alice; 
how  many  did  Alice  receive  ? 

1 8.  Frank  has  three  horses  and  one  saddle,  how  many 
more  horses  has  he  than  saddles  ? 

19.  Ella  had  three  playmates  and  gave  to  each  a  pear; 
how  many  pears  did  she  give  away  ? 

20.  Jacob  caught  three  rabbits  in  three  traps  ;  how  many 
did  he  catch  in  each  ? 

21.  If  you  should  lay  three  grains  of  corn  upon  the  floor 
and  a  mouse  should  come  and  carry  one  of  them  away  at  a 
time,  how  many  trips  would  it  have  to  make  to  carry  all  of 
them  away  ? 

22.  Place  three  grains  of  corn  upon  the  floor  ;  now,  if  a 
mouse  could  carry  away  only  one  grain  at  a  time,  how  many 
mice  would  be  required  to  carry  all  of  them  away  at  once  ? 
Make  picture-mice  and  prove  it. 

23.  Place  three  buttons  upon  the  table  ;  take  them  away 
two  at  a  time  ;  how  many  times  did  you  take  two  away ,? 


9 6  Science  and  Art  of  Education. 

24.  How  many  twos  in  three  ?     How  many  ones  ?     How 
many  threes  ? 

25.  Make  two  in  all  the  ways  you  can. 

26.  Make  ihree  of  ones  ;  how  many  does  it  take  ? 

27.  How   many  ones   in   two?     In    three?     How   many 
twos  in  two  ? 

28.  How  many  ones  in  one  half  of  two  ?    In  three  halves 
of  two  ? 

29.  How  many  twos  in  two  ones  ?     In  three  ones  ? 

30.  Take  three  buttons  and  lay  each  one  by  itself  ;  how 
many  separate  buttons  have  you  laid  ?    Count  them.    Each 
one  of  the  three  is  what  part  of  all  of  them  ?     (It  is  one  of 
the  three  equal  parts,  or  one  third.) 

31.  Show  me   one  third   of   three  yellow  squares  ;  two 
thirds   of   three   buttons  ;    three   thirds   of   three   picture- 
apples. 

32.  How  can  you  get  one  third  of  anything  ?     Can  you 
get  one  third  of  one  ?     How  ?     Do  it. 

33.  How  would  you  get  one  half  of  anything  ? 

34.  Which  is  the  larger  (or  greater),  one 
half   or  one  third  ?     Prove  it. 

35.  How  many  halves  in  one  and  one  half? 

36.  If  I  cut  an  apple  into  two  equal  pieces,  what  is  one 
of  the  pieces  called  ?     What  is  each  of  the  pieces  called  ? 

37.  Show  me  how  you  would  get  two  thirds  of  anything. 
Two  is  what  part  of  three  ?     One  is  what  part  of  two  ? 

38.  This  stick  (3  inches)  is   how  many  times  as  long  as 
that  (i  inch)  ?     How  can  you  find  out  ?     Do  it. 

39.  This  stick  (i  inch)  is  what  part  of   that  (3  inches). 
How  can  you  tell  ? 

40.  This  stick  (i  inch)  is  what  part  of  that  (2  inches.)  ? 

d.  Suggestive  Practical  Business  Problems. 

We  will  now  play  store.     John  may  be  the  merchant  and 
the  others  his  customers  or  buyers, 


Suggestions  for  Teaching  Numbers.  97 

1.  Sarah  may  buy  two  buttons,  at  a  cent  apiece,  and  give 
him  a  three-cent  piece  for  them.     How  much  change  will 
he  give  her  ? 

REMARK. — The  more  these  transactions  are  made  like  real 
business  the  more  interest  the  children  will  take  in  them. 

2.  Alice  may  buy  a  one-cent  candy  and  a  two-cent  candy 
How  many  cents  must  she  give  for  them  ? 

3.  Henry  buys  three  pencils  at  a  cent  each  ;  how  much 
money  will  pay  for  them  ? 

4.  Fannie  wants  three  cents'  worth  of  eggs,  and  the  eggs 
cost  a  cent   each  ;  how  many  will   she  get  ?     How  many 
would  she  get  for  two  cents  ?     Illustrate.     ^ 

5.  How  many  two-cent  rings  can  I  get  for  three  cents  ? 

6.  How  many  nuts  at  a  half-cent  each  could  you  get  for 
one  cent  ?     How  many  for  a  cent  and  a  half? 

7.  Fill  this  pint  measure  with  sand  and  pour  it  into  that 
quart  measure.     Did  it  fill  it  ?     Fill  it  again  and  pour  it  in. 
Is  it  now  full  ?    What  did  I  call  this  measure  ?    What  that  ? 
How  many  times  this  did  it  take  to  fill  that  ?     How  many 
pints  in  a  quart  ?     In  a  half-quart  ? 

8.  One  pint  is  what  part  of  a  quart  ?    Two  pints  are  what 
part  of  a  quart  ?     We  will  call  this  water  milk,  and  Annie 
may  sell  it  at  a  cent  a  pint. 

9.  Alice  wants   a   quart  and  gives  Annie   a   three-cent 
piece  ;  how  much  change  will  she  receive  ? 

10.  Sarah  wants  two  pints  ;  how  much  will  they  cost  ? 

11.  Jacob  wants  a  half-quart  and  has  a  two-cent  piece 
with  which  to  pay  for  it ;  give  him  the  change. 

12.  John  may  take  this  foot-measure  and  see  how  many 
such  could  be  made  of  that  yard-measure. 

13.  Henry,  you  may  tell  us  how  many  foot-measures  it 
takes  to  make  a  yard-measure,  or  a  yard.     Prove  it. 

14.  How  many  feet  make  a  yard,  or  are  in  a  yard  ?    How 
many  in  one  third  of  a  yard  ?    In  two  thirds  ?    In  one  half  ? 
Sarah  may  now  sell  tape  to  the  other  members  of  the  class. 


Science  'and  Art  of  Education. 


REMARKS. — Let  the  children  make  tape  of  newspapers,  by 
cutting  them  into  narrow  strips  and  sewing  the  ends  together. 

15.  Alice  buys  a  yard  that  costs  two  cents   and  a  yard 
that  costs  one  cent  ;  how  much  will  it  all  cost  ? 

1 6.  Anna  wants  a  third  of  a  yard  of   that  which  costs 
three  cents  a  yard  ;  how  many  cents  must  she  give  for  it  ? 
Prove  it  ? 

17.  Fannie  wants  a  cent's  worth  of  that  which  costs  three 
cents  a  yard  ?     How  much  will  she  get  ? 

1 8.  Peter  wants  a  yard  and  a  half  of  that  which  sells  at 
two  cents  a  yard  ;  how  much  money  will  pay  for  it  ? 

19.  Ella  had  three  yards  and   sold  one  third  of  them  ; 
how  many  had   she  left  ?     If  it  sold  at  three  cents  a  yard, 
what  did  she  get  for  what  she  sold  ? 

20.  When  a  quart  of-  milk  costs  two  cents,  what  does  a 
pint  cost  ? 

21.  How  many  pints  in  a  quart  ?     How  many  quarts  in 
three  pints  ? 

22.  How  many  feet  in  a  yard  ?     In  a   half -yard  ?    In  a 
third  of  a  yard  ? 

23.  One  foot  is  what  part  of  a  yard  ? 

24.  If  a  yard  of   tape   costs  three  cents,  what  does  one 
foot  of  it  cost  ?    What  two  thirds  of  a  yard  ? 

LESSON  ON  FOUR. 
a.   What  the  Puils  should  Discover. 


i.  3  +  1  = 

9-4-4= 

17.  |of4= 

25.  i  qt. 

2.  1+3= 

10.   4  -f-  2  = 

18.  iof  i  = 

26.  1  gal. 

3.    2  +  2  = 

II.    4  -4-  1  = 

19.  f  of  i  = 

27.  4  gills 

4.   2X2  = 

12.  4-3= 

20.   f  Of  I  = 

28.  i  pt. 

5.    1X4= 

13,  4  -s-"4= 

21.    |  Of  1  = 

29.  4  pk. 

6.  4—1  = 

14.  iof4= 

22.   i  Of  i  = 

30.  i  bu. 

7-  4-2  = 

15.  |of4= 

23.  4qts.= 

31.  i  pk. 

8.  4-3= 

j6.  I  of  4= 

24.  2  qts.  = 

33,  4  weeks 

Suggestions  for  Teaching  Numbers.  99 

b.  The  following  will  serve  as  examples  of  what  may  be 
given  as  seat-work  : 


1. 

III 

+  i 

•i 

10. 

iiii-*-ii     = 

18. 

i 

(i 

)  = 

2. 

I 

+  ni 

= 

II. 

ii 

u-i-i 

= 

19. 

1 

(i 

)  = 

3- 

II 

+  n 

= 

12. 

IIII-5-III     = 

20, 

| 

(i 

)  = 

4- 

II 

X  II 

= 

13- 

1111-4-1111  = 

21. 

| 

(i 

)  = 

5- 

I 

X  I  I  I  I 

= 

14. 

£ 

(mi) 

= 

22. 

^ 

(in 

i)= 

6, 

I  I  I  I 

—  I 

= 

15. 

•\ 

(mi) 

= 

23- 

I 

(nn)= 

7- 

mi 

—  II 

= 

1  6. 

I 

(mi) 

= 

24. 

1 

(nii)= 

8, 

1  1  1  1 

—  III 

= 

17- 

1 

(mi) 

= 

25- 

Hi 

)  = 

9- 

i  in 

—  IIII 

rs 

NOTE. — In  No.  25,  the  question  is,  What  part  of  one  is  one 
half  of  one  half  of  one  ?  and  by  dividing  each  of  the  two  halves  of 

a  given  line  or  square  into  two  equal  parts,  thus,      ^(    ^    ,    t 

I  ,the  answer  is  found  to  be  one  fourth. 

REMARK. — The  pupils  should  also  be  required  to  write  the 
foregoing  exercises  in  words,  either  in  the  question  or  in  the 
statement  form  or  in  both.  This  work  will  give  them  practice 
in  penmanship,  spelling,  and  language,  in  addition  to  that  of 
numbers.  Nos.  i,  10,  14,  15,  and  24,  for  example,  maybe  written 
as  follows:  (i.)  Three  and  one  are  how  many?  or  three  and 
one  are  four.  (10.)  How  many  twos  are  in  four?  (14.)  One 
half  of  four  ones  (or  of  four)  is  two  ones  (or  two).  (15.)  What 
is  one  third  of  four  ones?  (24.)  What  are  three  fourths  of  four 
ones,  or  of  four  (ones  being  understood)  ? 

c.  Suggestive  Questions  and  Problems. 

1.  Take  a  one  and  a  two.     How  many  ones  have  you 
taken  ?     How  many  threes  ? 

2.  Take  a  three   and  a   one.     How  many  ones  did  you 
take  ?     (Three  and  one  are  four.) 

3.  Give  me  a  two.     Give   me  another.     How  many  ones 
did  you  give    me?     How  many  ones  are   in   four?     How 
many  twos  ?     How  many  threes  ?  How  many  fours  ? 

4.  Show  me  one  four,  one  three,  one  two. 

5.  How  many  twos  in  three  ? 


Science  and  Art  of  Education. 


6.  One  half  is  what  part  of  one  and  one-half  ?     Of  two 
ones? 

7.  How  many  ones  in  three  halves  ?     In  four  halves  ? 

8.  How  many  feet  in  a  yard  ?     In  a  half-yard  ?     In  two 
thirds  of  a  yard  ? 

9.  How  many  pints  in  a  quart  ?     In  a  half-quart  ? 

10.  How  many  quarts  will  fill  this  gallon  measure  ?    How 
can  you  find  out  ?    Do  it.    We  will  call  this  water  milk,  and 
sell  it  at  four  cents  a  gallon. 

11.  Sarah  wants  a  quart  and  gives  a  two-cent  piece  to  pay 
for  it  ?  how  much  change  shall  she  receive  ? 

12.  Alice  wants  a  half -gallon  ;  how  many  cents  will  pay 
for  it  ? 

13.  Jacob  buys  two  pints  ;  what  will  they  cost  ? 

14.  Anna  wants  two  half-gallons  ;  how  much  money  will 
she  need  to  pay  for  them  ?    How  many  two-cent  pieces  will 
pay  for  them  ? 

15.  Here  is  a  measure  we  have  not  yet  used;  it  is  called  a 
peck,  and  is  used  for  measuring  apples,  peaches,  nuts,  corn, 
wheat,  etc.,  things  not  liquid  and  not  sold  by  the  pint  or 
quart.     Henry  may  fill  it  with  saw-dust  and  empty  it  into 
that  half-bushel.     Does  it  fill  it  ?    Peter  may  fill  it  and  also 
empty  it  into  the  half-bushel.     Is  the  half-bushel  now  full  ? 
How  many  pecks  make  (fill)  a  half-bushel  ?     How  many  a 
bushel  (whole  bushel)  ? 

We  will  now  sell  peaches,  at  a  dollar  a  bushel.  You  may 
get  the  money  (toy-money).  John  may  sell  them.  He  has 
no  peaches,-  but  he  may  make  believe  (pretend)  that  he  is 
selling  and  you  may  make  believe  that  you  are  buying. 

1 6.  Jacob    wants    two   pecks.      He   may   show   us   the 
money  he  will  give  for  them.     How  many  quarter-dollars 
has  he  ?     Has  he  enough  money  ?     Prove  it.     How  many 
half-dollars  would  pay  for  them  ?     Prove  it. 

17.  Peter  sells  pears,  at  two  dollars  a  bushel,  and  John. 


Suggestions  for  Teaching  Numbers. 


buys  a  peck.    He  may  get  the  money  to  pay  for  them.    Did 
he  get  enough  ? 

1 8.  Jacob  wants  a  bushel  and  a  peck  of  pears.     He  may 
get  the  money  to  pay  for  them.     Has  he  enough  money  ? 
How  can  you  tell  ? 

19.  Three   quarters  of   a  bushel  make  how  many  half- 
bushels  ?     How  many  pecks  ? 

20.  How  many  half-dollars  will  pay  for  three  quarters  of 
a  bushel  of  pears  ?     What  part  of  a  dollar  would  pay  for 
them  ? 

21.  Alice  wants  a  bushel  and  a  half  ;  how  much  money 
will  pay  for  them  ?     Prove  that  your  answer  is  right. 

22.  Sarah  sells   Henry  two  and  a  half  yards  of  cloth,  at 
one  dollar  a  yard  ;  how  many  dollars  will  pay  for  them  ? 
How  many  dollars  will  three  half -yards  cost  ?  how  many 
three  quarters  of  a  yard  ? 

23.  What  number  diminished  by  two  leaves  nothing  ? 

24.  From  what  number  can  I  take  one-half   and  have 
one  and  one  fourth  left  ? 

25.  From  what  number  can  I  take  two  and  one  half  and 
have  one  and  one  half  left  ? 

26.  What  number  added  to  one  makes  four? 

27.  What  number  added  to  one   and   one  half    makes 
three  ? 

28.  I  think  of  a  number  whose  half  is  two  ;  what  is  it  ? 

29.  What  number  taken  four  times  makes  four  ? 

30.  I  think  of  a  number  whose  fourth  part  is  one  ;  what 
is  it  ? 

31.  What  two  numbers  make  four?    What  three  num- 
bers? 

32.  What  number  taken   three   times,  and  ^one   added, 
makes  four  ? 

33.  What  number  doubled  makes  four?     What  three  ? 

34.  What  number  doubled,  and  one  added,  makes  three  ? 

35.  Make  four  in  all  the  ways  you  can,  mentally. 


102  Science  and  Art  of  Education* 

36.  Make  two  in  all  the  ways  you  can  ;  also  three. 

37.  What  is  one  half  of  one  ?  of  three  ? 

38.  What  is  one  third  of  one  ?  of  two  ?  of  four  ? 

39.  What    are  two   thirds    of    one  ?   of   two  ?  of  four  ? 
of  three? 

40.  What  are  two  fourths    of    one  ?      Three  fourths  of 
one  ?  Three  fourths  of  two  ?  of  three  ?  of  four  ? 

REMARK. — Whenever  it  is  possible  stories  should  be  made 
of  abstract  problems.  Stories  give  reality  and  interest  to  the 
work. 

LESSON  ON  FIVE. 


a.  i. 

2. 

3- 

4- 

4+1  = 

i  +  4  = 

3  +  2  = 

2  +  3  = 

1  8*. 

.|.  .|.  .,.  .|. 

IO  IT)  XT)  *O 

2 

3 

4 
5 

= 

29. 
30- 
31- 
32- 

*of 
iof 
fof 
*of 

2  = 

3  = 
3  = 
3  — 

5- 

2 

+ 

2 

+  i  = 

19. 

tot 

5 

= 

33- 

iof 

4  = 

6. 

2 

X 

2 

+  1  = 

20. 

iof 

5 

= 

34- 

fof 

4  = 

7- 

I 

X 

5 

s± 

21. 

fof 

5 

= 

35- 

|of 

4  = 

8. 

5 

X 

i 

= 

22. 

iof 

5 

= 

36. 

*of 

4  = 

9- 

5 

— 

i 

— 

23. 

Iof 

5 

:= 

37- 

iof 

5  = 

10. 

5 

— 

2 

= 

24. 

iof 

i 

= 

38- 

fof 

5  = 

ii. 

5 

— 

3 

= 

25- 

fof 

i 

= 

39- 

I  of 

5  = 

12. 

5 

— 

4 

= 

26. 

fof 

i 

= 

40. 

*of 

13- 

5 

— 

5 

= 

27. 

iof 

2 

= 

41. 

iof 

5  = 

14. 

5 

-r 

i 

= 

28. 

fof 

2 

= 

b.  Examples  of  Seat-work. 

REMARK. — For  the  seat-work  of  five  and  the  following  num- 
bers, until  the  children  can  use  figures,  the  notation  of  the 
numbers  preceding  five,  or  the  following,  may  be  used. 

1.  four  +  one  =  12.  five  —  four  = 

2.  one  +  four  =  13.  five  —  five  = 

3.  three  +  two  =  14.  five  -*-  one  = 

4.  two  -f  three  =  15.  five  -f-  two  = 

5.  two  +  two  -f  one  =  16.  five  •*-  three  = 

6.  two  x  two  4-  one  =  17.  five  -*-  four  = 

7.  one  +  two  x  two  =  18.  five  -*-  five  = 

8.  one  x  five  =  19.  one  half  of  five  = 

9.  five  —  one  =  20.  one  third  of  five  = 
10.  five  —  two  =  21.  two  thirds  of  five  = 
n.  five  —  three  =  22.  one  fourth  of  five  = 


Suggestions  for  Teaching  Numbers.  103 

23.  three  fourths  of  five  =  33.  one  fifth  of  four  = 

24.  one  fifth  of  one  =  34.  two  fifths  of  four  = 

25.  three  fifths  of  one  =  35.  three  fifths  of  four  = 

26.  five  fifths  of  one  =  36.  four  fifths  of  four  = 

27.  one  fifth  of  two  =  37.  one  fifth  of  five  = 

28.  three  fifths  of  two  =  38.  two  fifths  of  five  = 

29.  four  fifths  of  two  =  39.  three  fifths  of  five  = 

30.  one  fitfh  of  three  =  40.  four  fifths  of  five  = 

31.  two  fifths  of  three  =  41.  five  fifths  of  five  = 

32.  four  fifths  of  three  = 

c.  Suggestive  Questions  and  Problems. 

1.  Place  four  blocks  upon  the  table.     Place  another  on. 
How  many  are  on  now  ?     (You  have  placed  five  on.)    How 
many  did  you   place  on   first  ?      How    many  afterwards  ? 
How   many   altogether?      Then   four    and   one   are   how 
many  ? 

2.  Can  you  make  five  of   ones?     Try  it.     How  many 
does  it  take  ? 

3.  Can  you  make  five  of  twos  ?     How  many  does  it  take  ? 
Then  two  twos  and  one  are  how  many  ?     How  many  ones  ? 

4.  Can  you  make  five  of   threes?     How  make  does  it 
take  ?    One  three  and  one  two  are  how  many  ?    One  three 
and  two  ones  are  how  many  ? 

5.  Can  you  make  five  of    fours  ?      How  many  does  it 
take? 

6.  Make  five  in  all  the  ways  you  can  (in  your  mind) 
without  objects,  and  in  every  case  tell  the  result. 

7.  How  many  threes  are  in  four?      How  many  twos? 
How  many  ones  ? 

8.  What  is  one  half   of   four?  of   two?  of   one?     One 
third  of  three  ?  of  four  ?  of  one  ? 

9.  What  is  one  fourth  of  four  ?  of  three  ?  of  two  ?  of  one  ? 
One  third  of  two? 

10.  Divide  five  pebbles  into  five  equal  parts.     How  many 
have  you  in  each  ?     One  is  what  part  of  five  ?     How  many 
such  parts  are  in  five?     How  many  fifths  of  five  are  in 
five  ?     How  many  fifths  of  one  are  in  one  ? 

(UNIVERSITY 

OF 

''v 


IO4 


Science  and  Art  of  Education. 


ii.  How  many  times  can  you  find  two  fifths  of  one  in 
one? 

REMARK.—  Problems  of  this  kind  should  at  this  stage  of  the 
pupil's  progress  be  solved  with  diagrams.     Solution  of  prob- 


lem  u  : 


The  answer  is 


12.  How  often  can  you  find  three  fifths  of  one  in  one? 

.1% 
Solution: 


i       % 

JJJ  *  or  rrrrrv  m. 


13.  How  often  can  you  find  four  fifths  of  one  in  one  ? 
Prove  it. 

14.  How  often  can  you  find  two  thirds  of  one  in  one  ? 

i    H 
Prove  it.     Solution  : 


15.  What  is  one  half  of  five  ?    One  third  of  five  ?     One 
fourth  of  five  ?     One  fifth  of  five  ?     Solution  of  first : 


i  +  4  +  *  + 1  +4  =  2*. 


1  6.  What  are  two  thirds  of  five?     Three  fourths  of  five? 
Two  fifths  of  five  ?     Solution  of  first  : 


4-  -I  =  1-k* 

I      o  Oo* 

17.  I  know  a  number  to  which  if  I  add  three  it  will 
make  five  ;  what  is  it  ? 

1  8.  I  know  a  number  that  contains  two  twos  and  one 
one  ;  what  is  it  ? 

19.  I  think  of  a  number  to  which  if  I  add  four  it  will 
make  five  ;  what  is  it  ? 

20.  I  know  a  number  whose  half  is  two  ;  what  is  it  ? 


Suggestions  for  Teaching  Numbers.  105 

21.  I  know  a  number  whose  half  added  to  it  makes  three; 
what  is  it  ? 

22.  From  what  number  can  I  take  its  third  and  have  two 
left? 

23.  If  to  a  certain  number  I  add  its  two  thirds,  the  sum 
will  be  five  ;  what  is  the  number  ? 

24.  What  number  added  to  one  and  one  half  makes  four  ? 

25.  I  think  of  a  number  that  is  three  less  than  five  ;  what 
is  it? 

26.  What  number  is  two  less  than  three  ? 

27.  If  from  a  certain  number  I  take  its  fourth,  three  will 
be  left ;  what  is  it  ? 

28.  What  number  doubled  makes  five  ? 

29.  Three  times  a  number  and  twice  the  number  make 
five  ;  what  is  the  number  ? 

30.  What  number  doubled  and  its  half  added  makes  five  ? 

31.  What  number  increased  by  its  fourth  equals  five  ? 

32.  What  number  lacks  two  of  being  five  ? 

33.  What  two  unlike  numbers  make  five  ?     What  unlike 
numbers  make  four  ?     What  like  numbers  ? 

34.  I  buy  apples  at  two  cents  each  and  they  cost  me  four 
cents  ;  how  many  do  I  buy  ? 

35.  I  bought  candies  at  one  cent  each,  and  out  of  three 
cents  received  one  cent  change ;  how  many  did  I  buy? 

36.  I  paid  four  cents  for  two  pencils  ;  how  much  did 
they  cost  me  apiece  ? 

37.  I  bought  two-cent  oranges,  and  out  of  five  cents  re- 
ceived one  cent  change  ;  how  many  did  I  buy  ? 

38.  Sarah  had  five  two-cent  pieces  and  gave  one  to  each 
of  three  boys  ;  how  many  had  she  left  ?     How  many  cents 
could  she  get  for  them  ? 

39.  A  bird  laid  five  eggs  and  hatched  them  all  but  four ; 
how  many  did  it  hatch  ? 

40.  Two  boys  and  three  girls  went  coasting  ;  the  number 
of  boys  is  what  part  of  that  of  the  girls  ?     By  what  part  of 


106  .          Science  and  Art  of  Education. 

their  number  should  that  of  the  boys  have  been  increased 
to  have  made  it  equal  to  that  of  the  girls  ? 

41.  Jane  has  four  ducks  and  three  pigeons  ;  how  many 
times  as  many  ducks  has  she  as  pigeons  ?     The  number  of 
pigeons  is  what  part  of  that  of  the  ducks  ? 

42.  Henry's  book  cost  him  three  cents,  and  his  pencil 
one  third  as  much  ;  how  much  did  both  cost  ?    The  differ- 
ence in  cost  of  the  two  is  what  part  of  the  cost  of  the  book  ? 
The  cost  of  the  pencil  is  what  part  of  the  difference  ? 

43.  One  is  what  part  of  two  ?  of  three  ?  of  five  ? 

44.  Two  is  what  part  of  three  ?  of  four  ?  of  five  ? 

45.  Three  is  how  many  times  two  ?     Three  is  what  part 
of  three  ?  of  four  ?  of  five  ? 

46.  Four  little  birds  were  in  a  nest  and  one  half  of  them 
flew  away  ;  how  many  remained  ? 

47.  Three  boys  are  playing  ball ;  what  part  of  their  num- 
ber must  be  added  to  them  to  make  it  five  ? 

48.  How  many  two-cent  postage-stamps  can  you  get  for 
five  cents  ? 

49.  How  many  yards  of  tape,  at  three  cents  a  yard,  can 
you  get  for  five  cents  ?    What  part  of  a  yard  for  two  cents  ? 

50.  If  your  mother  should  send  you  to  the  store  with  five 
cents,  to  buy  thimbles  that  cost  four  cents  each,  how  many 
could  you  get  ?     How  much  change  would  you  get  ? 

51.  With  five  cents  buy  all  the  two-cent  lemons  you  can? 
How  many  can  you  get  ?     Prove  it. 

52.  A  bushel  of  apples  costs  three  quarters  of  a  dollar  ; 
how  many  bushels  can  you  get  for  two  dollars  ?  for  three 
dollars  ?     For  two  and  one  half  dollars  ? 

53.  A   bushel   of   pears   costs   two   dollars  ;  how   many 
bushels  could  you  get  for  five  dollars?  for  two  and  a  half 
dollars  ?     What  part  of  a  bushel  could  you  get  for  one  and 
a  half  dollars?  for  three  fourths  of  a  dollar?  for  a  half 
dollar  ?     How  many  pecks  could  you  get  for  one  and  one 
fourth  dollars  ? 


Suggestions  for  Teaching  Numbers.  107 

« 

54.  A  peck  of  plums  costs  a  half  dollar  ;  how  many  half 
bushels  could  you  get  for  a  dollar  and  a  half.     How  many 
bushels  for  three  dollars  ? 

55.  When  a  half  bushel  of  quinces  costs  one  and  one  half 
dollars,  how  much  does  a  peck  cost  ?  how  much  a  bushel  ? 
What  part  of  a  bushel  could  you  get  for  a  half  dollar  ?  for 
two  dollars  ? 

56.  When  a  gallon  of  honey  costs  two  dollars,  what  part 
of  a  gallon  can  be  had  for  a  half  dollar  ?   for   a  dollar  ? 
How  many  quarts  for  a  dollar  and  a  half  ?     What  part  of  a 
dollar  would  a  pint  cost  ? 

57.  At  five  dollars  a  yard,  what  part  of  a  yard  of  cloth 
can  be  bought  for  three  dollars  ?  what  for  two  and  a  half 
dollars  ?  for  one  dollar  ? 

58.  A  quince  and  a  peach  together  cost  three  cents  ;  how 
much  did  each  cost,  if  the  quince  cost  twice  as  much  as  the 
peach  ? 

59.  Two  oranges  cost  five  cents  ;  how  much  did  each 
cost,  if  one  cost  a  cent  more  than  the  other  ? 

60.  Three  times  a  number  less  twice  the  number  equals 
one  ;  what  is  the  number  ? 

6 1.  Once  a  number  and  half  the  number  equal  three  ; 
what  is  the  number  ? 

62.  There  are  three  times  as  many  geese  in  a  pond  as 
ducks;  if  there  are  three  geese,  how  many  are  there  alto- 
gether ? 

63.  Sarah  has  three  canary-birds  more  than  Anna  ;  how 
many  have  both,  if  Anna  has  one  ? 

64.  In   three   halves,   how  many  ones  ?     Three  halves 
equal  what  part  of  two  ? 

65.  In  five   thirds   how 
many  ones  ?     How  many  , 
halves  ? 

REMARK.  —  The    second 
part  of   question   No.   65   may  be  solved  with   the  following 
diagrams : 


io8 


Science  and  Art  of  Education. 


66.  In  five  fourths  how  many  ones  ?  how  many  halves  ? 
Solution  of  second  by  diagrams  : 


67.  One  and  one  half  is  what  part  of  two  ?    Solution  : 

mn  *-*> 

68.  One  and  one  fourth  is  what  part  of  five  ?    Solution  : 


69.  How  many  thirds  in  one  half  ?    Solution  : 


70.  One  third  is  what  part  of  one  half  ?   Solution: 
One  third  contains  two  of  the  three  equal  parts  of 
one  half,  and  is  therefore  two  thirds  of  it. 

71.  How  many  fourths  in  one  half? 

72.  One  fourth  is  what  part  of  one  half? 

73.  How  many  times  is  one  half  in  two  thirds? 
Solution:  Examining  the  diagram,  we  find  that 
one  half  of  it  contains  three  blocks,  and  two  thirds 
four;  the  problem,  therefore,  is  reduced  to  finding 

the  number  of  times  three  blocks  are  found  in  four  blocks. 

Ans.   i£. 

74.  One  third  is  what  part  of  two  thirds  ? 

75.  Two  fourths  are  what  part  of  three  fourths  ? 

76.  Three  fifths  are  what  part  of  four  fifths  ? 

77.  One  half  is  what  part  of  three  fourths? 


Suggestions  for  Teaching  Numbers. 


109 


LESSON  ON  Six. 
a.   What  the  Pupils  Must  Discover 


2. 

3- 
4- 
5- 
6. 

7- 
8. 

9- 

i+5= 

2+4= 
3  +  3= 
3x2= 
2x3  = 
1x6= 
6-1  = 

n. 

12. 

13- 
14. 
15- 

1  6. 

17. 
18. 
19. 

6-2  = 

6-5= 
6-6= 
6-*-i  = 

6-5-2  = 

6-5-3= 
6-5-4= 
6-5-5  = 
6-5-6= 

21. 

22. 

23- 
24. 
25. 
26. 
27. 
28. 
29. 

f  of  6= 
iof  6= 
f  of  6= 
iof  6= 
f  of  6= 
fof  6= 
fof  6= 
jfof  6= 
iof  6= 

31- 

32- 
33- 
34- 
35- 
36. 
37- 
38. 

39- 

iof  6= 
fof  6= 
*  of  6= 

f  ofi  = 

Iof  i  = 
fof  i  = 

iof  2  = 

iof  5  = 

41. 

42. 

43. 
44. 
45- 
46. 
47- 

fof  2: 

fof  4= 

|of  4: 

I  °,f  5: 
fof  5 

fof  6: 

fof  5= 

10.  6—3=     20.  iof6=    30.  f  of  6=    40.  |  of  2= 
b.  Examples  of  Seat-work. 


1.  five  +  one      =          8.  one  x  six 

2.  one + five      =          9.  six— one 

3.  four  +  two     =         10.  six— three 

4.  two  +  four    =         ii.  six— two 

5.  three  -f  three  =        12.  six— five 

6.  three  x  two  =         13.  six— six 

7.  two  x  three  =         14.  six-*-one     = 

21.  two  halves  of  six      =        32. 

22.  one  third  of  six         =         33. 

23.  two  thirds  of  six       =         34. 

24.  one  sixth  of  six         =         35. 

25.  two  thirds  of  six       =         36. 

26.  three  thirds  of  six     =         37. 

27.  four  sixths  of  six      =         38. 

28.  five  sixths  of  six       =         39. 

29.  one  fourth  of  six      =         40. 

30.  three  fourths  of  six  =        41. 

31.  one  fifth  of  six          =        42. 


=  15.  six-*-two             = 

=  1 6.  six -s- three          = 

=  17.  six-^four 

=  18.  six-5-five 

=  20.  one  half  of  six  = 


three  fifths  of  six  = 

four  fifths  of  six  = 

one  sixth  of  one  = 

three  sixths  of  one  = 

four  sixths  of  one  = 

one  sixth  of  two  = 

one  sixth  of  three  = 

one  sixth  of  four  = 

one  sixth  of  five  = 

three  sixths  of  five  = 

five  sixths  of  five  = 
etc.,  etc. 


r..  Suggestive  Questions  and  Problems. 
i.  Take  five  cubes.     Take  another.     How  many  alto- 


Science  and  Art  of  Education. 


gether  have  you  taken  ?     (You  have  taken  six.)     Five  and 
one  are  how  many  ? 

2.  Four  and  two  are  how  many  ?     Three  and  two  ? 

3.  Three  and    three    are   how  many   ones?  how  many 
twos  ? 

4.  Six  ones  are  how  many  twos  ?  how  many  threes  ? 

5.  How  many  fours  in  six  ? 

6.  Make  six  of  ones  ?  how  many  does  it  take  ? 

7.  Make  six  of  twos  ?  how  many  does  it  take  ? 

8.  Make  six  of  threes  ?  how  many  does  it  take  ? 

9.  Make  six  in  all  the  ways  you  can  mentally,  and  in 
every  case  tell  the  result. 

10.  Three  twos  are  how  many  ones  ? 

11.  Two  threes  are  how  many  ones  ? 

12.  Six  ones  are  how  many  twos?  how  many  threes? 

13.  I  know  a  number  whose  third  is  one;  what  is  it  ? 

14.  I  think  of  a  number  which  doubled  makes  six;  what 
is  it? 

15.  I  think  of  a  number  whose  half  added  to  it  makes 
six;  what  is  it  ? 

1 6.  If  to  twice  a  number  I  add  two,  it  makes  six  ;  what  is 
the  number  ? 

17.  From  what  number  can  I  take  its  half  and  have  one 
left? 

1 8.  What  number  diminished  by  its  third  leaves  four  ? 

19.  If  to  a  certain  number  I  add  its  fifth,  it  makes  six; 
what  is  the  number  ? 

20.  From  what  number  can  I  take  half  of  four  and  have 
four  left  ? 

21.  If  to  a   certain   number  I  add  a  third  of  three,  it 
makes  two;  what  is  the  number  ? 

22.  Three  times  a  number  less  once  the  number  is  four  ; 
what  is  the  number  ? 

23.  What  equal  numbers  make  six  ?    What  unequal  num- 
bers? 


Suggestions  for  Teaching  Numbers. 


24.  How   many  fourths    in    a   half  ?  in    a   fourth    and  a 
half? 

25.  How     many    sixths    in     one?    in    a    half? 
in  a  third  ? 

26.  A  half  and  a  third  equal  how  many  sixths  ? 

27.  A  half,  a  third,  and  a  sixth  are  how  many  ones  ? 

28.  Two  thirds    are    how   many    sixths  ?     Three 
equal  how  many  thirds  ?  how  many  halves  ? 

29.  Four   sixths    equal    how   many  thirds  ?  how[ 
many  halves  ? 

30.  Five    sixths    equal    how  many    thirds  ?    how  many 
halves ? 


31.  At  two  cents  a  yard,  how  many  yards  of  tape  could 
you  buy  for  six  cents  ? 

32.  How  much  money  will  pay  for  four  apples  at  a  half- 
cent  each  ?  at  a  fourth  of  a  cent  each  ? 

33.  If  plums   sell  at* a  fourth  of  a  cent  each,  how  much 
would  six  cost  ? 

34.  Sarah  can  walk  two  miles  an  hour  and  Helen  three  ; 
!.o\v  long  would  it  take  each   to  walk  to  a  town  six  miles 
distant  ?     If  they  should  start  together,  how  far  apart  would 
they  be  at  the  end  of  two  hours  ?     If  they  should  start  to- 
gether but  go  in  opposite  directions,  how  far  apart  would 
they  be  in  one  hour  ? 

35.  Alice  went  to  the  grocery  with  six  cents  ;  she  bought 
pears  with  one  third  of   them,  cherries  with    one   half  of 
them,  and  chestnuts  with  the  remainder  ;  how  much  money 
did  she  give  for  each  ? 

36.  If  fish-hooks  cost  a  half-cent  each,  how  many  can 
Charles  buy  for  three  cents  ? 

37.  Henry  bought  rabbits  at    a  half-dollar   each  ;    Kow 
many  did  he  get  for  two  dollars  ? 

38.  When  hickory-nuts  sell  at  four  cents  a  quart,  how 


Science  and  Art  of  Education. 


many  pints  can  John  get  for  six  cents  ?  How  many  for  two 
cents  ? 

39.  Jennie  and  Cora  went  to  the  cellar  for  apples  ;  how 
many  did  each  get,  if  Cora  had  twice    as  many  as  Jennie, 
and  both  had  six  ? 

40.  If  a  yard  of  muslin  costs  six  cents,  what  does  a  foot 
of  it  cost  ? 

41.  One  sixth  is  what  part  of  three  sixths  ?  of  two  sixths  ? 
of  five  sixths  ? 

42.  One   sixth    is  what   part   of   one  f  „ 
half?     Solution  by  diagram  : 

43.  One    sixth   is    what     part   of   one   ^ 

fourth  ?     Solution  by  diagram  :  (Tfj  |   ]  —  i  —  1=% 


44.  What  part  of  one  is  one  half  of  one    ^ 

third  ?     Solution  :  I    I    I    I  one  of  the  blocks,  being  a  half  of 
of    a    third,   is   a  |^l    I    '  sixth  of  one,  or  of  the  whole. 

45.  One  half  of  one  half  is  what  part  of  one  ? 


H\ 

^  H. 


-t— I  or> 

46.  One  third  of  one  half  is  what  part  of  one  ? 
Solution  :   |   \    \    \    \    \    |,  or     %. 

47.  What  is  one  half  of  two  thirds  ?  of  three  thirds  ? 

REMARK  i.— It  is  not  deemed  necessary  to  indicate  what 
the  pupils  should  discover,  nor  to  give  examples  of  seat-work, 
further  than  the  number  six. 

2. — From  here  on   figures  may  gradually  be  introduced. 

Suggestive  Questions  and  Problems  on  Seven. 

1.  Put  four  cubes  upon  the   table  ;  put  three  more  on. 
How  many  ones  have  you  put  on  ?     (Four  ones  and  three 
ones  are  seven  ones.) 

2.  Three  twos  and  one  are  how  many  ? 

3.  Five  and  two  are  how  many  ? 

4.  Two  threes  and  one  a.re  how  many  ? 


Suggestions  for  Teaching  Numbers.  1 1 3 

Seven  ones  are  how  many  twos  ?  how  many  threes  ? 

6.  What  number  is  three  less  than  seven  ? 

7.  What  number  added  to  five  makes  seven? 

8.  I  think  of   a  number  whose   double   and  one  added 
make  seven  ;  what  is  it  ? 

9.  What  number  is  that  whose  half   added   to  it  makes 
six  ? 

10.  What  is   one   seventh   of    seven  ?    What  are  three 
sevenths  of  seven  ?  five  sevenths  ?  seven  sevenths  ? 

11.  Two  thirds  of  three  apples  and  three  fourths  of  four 
apples  are  how  many  apples  ? 

12.  Jane  found  one  half  of  four  chestnuts  and  Alvira  two. 
thirds  of  six  ;  how  many  did  both  find  ? 

13.  Of  tape  costing  a  half-cent  a  yard,  Hannah  bought 
one  third  of  three  yards,  Eva  three  fourths  of  four  yards, 
and  Emily  five  sixths  of  six  yards  ;  how  much  did  they  all 
pay? 

14.  One  half  of  four  and  two  thirds  of  six  are  how  many 
ones  ?  how  many  twos  ?  how  many  threes  ? 

15.  Four  sevenths  of   seven  and  three  fifths  of  five  are 
how  many  ones  ?  how  many  twos  ?  how  many  threes  ? 

16.  Make  seven  of  twos  ;  how  many  does  it  take  ? 

17.  Make  seven  of  threes  ;  how  many  does  it  take  ? 

18.  Make  seven  in  all  the  ways  you  can  mentally,  and  in 
each  case  state  the  result. 

19.  How  many  two-cent  postage-stamps  could  you  buy 
with  seven  cents  ? 

20.  An  orange  costs  three  cents  and  a  lemon  two  thirds 
as  much  ;  how  much  do  both  cost  ? 

21.  How  many  three-cent  and  four-cent  pies  could  you 
buy  with  seven  cents  ? 

22.  How  many  pints  in  three  quarts  ?  How  many  gills  in 
a  pint  and  a  half  ? 

23.  How  many  feet  in  two  yards  ?  in  two-thirds   of  a 
yard? 


1 1 4  Science  and  Art  of  Education. 

24.  If  two  cakes  cost  six  cents,  what  is  the  cost  of  each  ? 

25.  John  has  six  pears  which  he  wishes  to  share  with  his 
two  companions  ;  how  many  will  he  give  to  each  ?  What 
part  of  them  will  he  keep  ? 

REMARK. — A  square  has  four  equal  sides  and  four  right 
angles.  When  the  sides  are  one  inch,  it  is  a  square  inch ;  when 
one  foot,  a  square  foot ;  when  a  yard,  a  square  yard,  etc. 

26.  How  many  squares,  an  inch  on  each  side,  could  you 
cut  from  a  piece  of  paper  two  inches  long  and  one  inch 
wide? 

27.  How  many  squares,  two  inches  on  each  side,  could 
you  make  from  a  piece  of  paper  four  inches  long  and  one 
inch  wide  ? 

28.  How  many  squares,  a  yard  on  each  side,   could  you 
cut  from  a  piece  of  muslin  three  yards  long  and  two  yards 
wide  ? 

29.  Henry  borrowed  a  book  from  the  town  library,  at  a 
half-cent  a  week,  and  kept  it  until  the  hire  of  it  amounted 
to  three  and  a  half  cents  ;  how  long  did  he  keep  it  ? 

30.  John  has  two  three-cent  pieces;  how  many  quarts  of 
milk,  at  two  cents  each,  can  he  get  for  them  ? 

31.  Mrs.  Smith  borrowed  Mrs.  Brown's  sewing-machine, 
at  a  quarter  of  a  dollar  a  week,  and  kept  it  a  month  ;  how 
much  did  she  owe  Mrs.  Brown  for  the  use  of  it  ? 

32.'  Mr.  Stone  hires  out  his  horse  at  the  rate  of  three 
dollars  for  two  days  ;  how  much  would  he  charge  for  the 
use  of  it  one  day  ?  How  much  for  three  days  ? 

33.  If  two  quarts  of  milk  cost  four  cents,  what  will  three 
quarts  cost  ? 

Suggestive  Questions  and  Problems  on  Eight. 

i.  How  many  ones  in  seven  ?  How  many  twos  ?  How 
many  threes  ?  How  many  fours  ?  How  many  fives  J  How 
many  sixes  ?  How  many  sevens  ? 


Suggestions  for  Teaching  Numbers.  1 1 5 

2.  Put  one  to  seven  and  how  many  have  you  ?     (Seven 
and  one  are  eight.) 

3.  Place  eight  cubes  upon  the  table  and  divide  (separate) 
them  into  two  equal  groups.     How  many  have  you  in  each 
group  ?     What  part  of  the  whole  ? 

4.  Divide  eight  cubes  into  four  equal  groups  and  tell  me 
how  many  you  have  in  each  group,  also  what  part  of  the 
whole. 

5.  Divide   eight   cubes   into  eight  equal  groups.     How 
many  have  you  in  each  ?  what  part  of  the  whole  ? 

6.  See  how  many  groups  of  three  you  can  find  in  eight ; 
how  many  of  five  ;  of  sixe  ;  of  seven. 

7.  Five  balls  and  three  balls  are  how  many  balls  ? 

8.  Eight  less  two  are  how  many  ? 

9.  Two  and  six  are  how  many  ?     How  many  more  than 
four  ?     How  many  more  than  seven  ? 

10.  Two  fours  are  how  many  more  than  three  twos  ? 

11.  One  is  how  much  less  than  one  half  of  two  ? 

12.  What  is  the  difference  between  three  and  two  thirds 
of  six  ? 

13.  See  how  many  quarts  of   sand   will   fill   this   peck 
measure. 

14.  What   is  the  larger  measure,    a   peck  or  a  gallon  ? 
what  is  the  difference  ? 

15.  You  may  now  find  how  many  pecks  of  sand  (or  saw- 
dust) will  fill  this  half-bushel.     How   many  would   fill  a 
bushel  ?     How  many  half-bushels  in  a  bushel  ? 

16.  How  many  pints  of  chestnuts,  at  four  cents  a  quart, 
can  you  buy  for  six  cents  ?     How  many  for  two  cents  ? 

17.  When  milk  sells  at  eight  cents  a  gallon,  how  much 
would  two  quarts  cost  ?     How  much  a  pint  ? 

1 8.  Helen  bought  a  yard  and  a  third  of  six-cent  muslin  ; 
how  much  did  she  pay  for  it  ? 

•  19.  Margaret  bought  plums  at  four  cents  a  quart,  ho\v 


1 1 6  Science  and  Art  of  Education. 

much  did  she  pay  for  one   fourth   of  a   peck?    for   one 
eighth  of  a  peck  ?  for  a  pint  ? 

20.  How  many  eighths  in  one  half?  in  one  fourth  ?  in 
two  halves  ?  in  three  fourths  ? 

21.  How  many  more  eighths  in  two  fourths  than  in  one 
half? 

22.  How  many  eighths  in  one  half,  one  fourth, 
eighth  ? 

23.  Which  is  the  larger,  one  half  or  one  third? 
What  is  the  difference  ? 

24.  Nora  bought  two  thirds  of  a  yard  of  lace  at  one 
store  and  one  half  of  a  yard  at  another  ;  how  many  yards 
altogether  did  she  buy  ? 

25.  How  many  months  in  eight  weeks  ? 

26.  Henry  was  hired  to  Mr.  Carpenter  at  four  dollars  a 
month  ;  how  much  did  he  receive   for  three  weeks  ?  for 
five  weeks  ?  for  three  days  ?  for  a  week  and  a  half  ? 

27.  Mr.  Clay  hired   Mr.  Thome's  horse  at  the   rate   of 
eight    dollars  for  six  days  ;  he  used  the  horse  four  days. 
How  much  did  he  owe  Mr.  Thorne  ? 

28.  Joseph  borrowed  five  dollars  of  Philip,  agreeing  to 
pay  a  half-cent  a  month  for  every  dollar  borrowed  ;  if  he 
kept  the  money  two  months,  how  much  did  he  owe  for  the 
use  of  it  ? 

29.  Alfred   rented  two  books  from  the  library;  the  first 
was   worth   one   dollar,    the   second   two   dollars.      If   he 
paid  a  cent   a  week  for  the  first  and  two  cents  for   the 
second,  how  much  did  he  owe  at  the  end  of  two  and  a  half 
weeks  ? 

30.  One   is   what   part  of   five  ?    of    six  ?  of   seven  ?  of 
eight  ? 

31.  Two  is  what  part  of  six  ?  of  seven  ?  of  eight  ? 

32.  Three  is  what  part  of  six  ?  of  seven  ?  of  eight  ? 

33.  Four  is  what  part  of  five  ?  of  six  ?  of  seven  ? 

34.  Five  is  what  part  of  six  ?  of  seven  ?  of  eight  ? 


Suggestions  for  Teaching  Numbers.  117 


' 


35.  Six  is  what  part  of  seven  ?  of  eight  ? 

36.  Seven  is  what  part  of  eight  ?  Seven  is   how   many 
halves  of  eight  ? 

37.  If  you  had  one  third  of  two  yards  of  ribbon,  what 
part  of  a  yard  could  you  make  of  them  ? 

38.  Three  fourths  of  two  quarts  of  peanuts  would  make 
how  many  whole  quarts  ?  how  many  pints  ? 

39.  The  surface  of  anything — a  piece  of  paper  or  board, 
for  example — is  the  outside  of  it.     A  square  surface  an  inch 
on  each  side  and  all  the  angles  of  which  are  right  angles,  is 
I    I    ||  called  a  square  inch  ;  one  foot  on  each  side,  a  square 
Mil  foot,  etc.     A  board  three  feet  long  and  two  feet 
wide  contains  how  many  square  feet  ? 

40.  How  many  square  inches  could  you  cut  from  a  piece 
of  paper   three  inches  long  and  three  inches  wide  ?  How 
many  from  one  four  inches  long  and  two  inches  wide  ? 

41.  How  many  pieces  of  paper  two  inches  long  and  one 
inch  wide  could  be  made  from  a  piece  three  inches  long 
and  two  inches  wide  ? 

42.  A  piece  of  sheeting  one  yard  long  and  two  thirds  of 
a  yard  wide   contains  how  many  square  feet  ?   what  part 
of  a  yard  ? 

43.  How  many  square  feet  in  a  piece  of   cardboard  a 

half-yard  square  ? 

REMARK.— A  block  all  of  whose  surfaces  are  equal  squares  is 
a  cube.  If  the  sides  of  the  squares  are  one  inch  the  block  is  a 
cubic  inch ;  if  they  are  a  foot  it  is  a  cubic  foot,  etc. 

44.  I  have  a  cubical  block  of  wood  each  of  whose  edges 
is  two  inches  in  length  ;  how  many  cubical  blocks  whose 
edges  are  one  inch  could  be  made  of  it  ?     How  many  such 
could  be  made  of  a  block  two  inches  long  and  wide  and 
one  inch  thick?     How  many  of  one  six  inches  long,  one 
inch  wide,  and  half  an  inch  thick  ? 


Scienct  arid  Art  of  Education. 


45.  A  bushel  of  cloverseed  costs  four,  dollars  ;  what  is 
the  cost  of  a  peck  ?  of  a  quart  ? 

46.  One  fourth  is  what  part  of  three  fourths  ? 

47.  Two  fifths  are  what  part  of   three  fifths?   of  four 
fifths  ? 

48.  One  sixth  is  what  part  of  five  sixths  ?  of  two  sixths  ? 

49.  Three  sixths  are  what  part  of   four  sixths?    of  six 
sixths  ? 

50.  Four  sevenths  are  what  part  of  six  sevenths?     One 
half  is  what  part  of  four  sevenths  ? 

51.  One  half  is  what  part  of  five  eighths  ?   Three  eighths 
equal  what  part  of  one  half  ? 

52.  One  fourth   is   what   part  of   six  eighths?    of   two 


thirds  ? 


53.  One  sixth  is  what  part  of  one  fourth  ?    Solution  by 


diagram  : 


54.  One  seventh  is  what  part  of  one  sixth  ?     Solution  by 


diagram : 


55.  One  eighth  is  what  part  of  one  fifth  ?    Solution  by 


diagram  : 


-K. 


Suggestions  /or  Teaching  Number $*  tig 


Suggestive  Questions  and  Problems  on  Nine* 

1.  Two  threes  and  one  two  are  how  many?   how  many 
ones? 

2.  Three  twos  less  two  threes  are  how  many  ? 

3.  Two  fours  less  two  thirds  of  six  are  how  many  ?  how 
many  twos  ? 

4.  Which  is  the  larger,  four  twos  or  two  fours  ? 

5.  Four  twos  are  equal  to  how  many  ones  ? 

6.  If  to  eight  ones  you  add  one  one,  how  many  ones 
have  you  ?     (Eight  and  one  are  nine.) 

7.  How  many 'threes  can  you  find  in  nine  ones,  or  nine? 

8.  Nine    contains     how     many     twos  ?    fours  ?     fives  ? 
sixes  ?  sevens  ?  eights  ? 

9.  How  can  you  get  one  third  of  nine  ?    What  are  two 
thirds  of  nine  ? 

10.  Name  the  sums  of  the  following  numbers  as  quickly 
as  you  can  :  Three  and  four  ;  two  and  six  ;  five  and  three  ; 
two  and  seven  ;    four  and  four ;   one  and  four ;   six   and 
three;  etc. 

11.  Name  the  differences   between   the  following  num- 
bers :  Three  and  five  ;  two  and  six;  one  and  four  ;  two  and 
seven  ;    five  and  eight  ;    four  and  nine  ;    one  and  eight ; 
seven  and  nine  ;  etc. 

12.  From   eight  take  two  threes;  from  nine  three  take 
twos  ? 

13.  I  know  a  number  which  doubled  and   one   added 
makes  this  nine  ;  what  is  it  ? 

14.  Add  one  third  of  nine  and  three  fourths  of  four. 

15.  Into  what  like  numbers  can  you  divide  eight  ?   nine  ? 
six  ? 

1 6.  Three  fourths  of  eight  and  one  third  of  nine  equal 
how  many  threes  ? 

17.  Make  nine  in  all  the  ways  you  can  mentally,  and  in 
each  case  tell  the  result. 


Science  and  Art  of  Education. 


1 8.  In  three  yards  how  many  feet? 

19.  How  many  yards  in  five  feet  ?  in  eight  feet  ? 

20.  What  number  is  that  whose  third  is  three  ? 

21.  If  to  one  third  of   a  number  I  add    two,  the    sum 
will  be  three  ;  what  is  the  number? 

22.  Three  miles  added  to  three  fourths  of  the  distance 
Samuel  rode  on  his  bicycle  make  nine  miles  ;  how  far  did 
he  ride  ? 

23.  If  from  four  times  the  number  of  quarts  of  chest- 
nuts Henry  gathered  three  be  substracted,  five  will  be  left  ; 
how  many  did  he  gather  ? 

24.  Five  times  the  money  Sarah  received  for  making  a 
dress  added  to  two  dollars  equal  seven  dollars  ;  how  much 
did  she  receive  for  her  work  ? 

25.  Three  fourths  of    eight   cents  is  two  thirds  of   the 
price  of  a  gallon  of  milk  ;  what  is  the  price  ? 

26.  It  requires  two  thirds  of  nine  yards  of  goods  to  make 
Ella  a  dress,  and  this  is  three  fourths  of  the  number  re- 
quired to  make  one  for  Stella ;  how  many  yards  does  Stella 
require  ? 

27.  Elmer  is  twice  as  old  as  Carrie,  and  the  sum  of  their 
ages  is  nine  years  ;  required  the  age  of  each. 

28.  From  four  twos  take  two  thirds  of  nine,  and  what  is 
the  result  ? 

29.  How  many  square  yards  of  carpet  would  be  required 
to  cover  a  floor  nine  feet  long  and  six  feet  wide  ?     What 
would  be  the  cost  of  the  carpet  at  a  dollar  and  a  half  a  yard  ? 

REMARK. — The  pupils  should  by  this  time  have  learned  that 
the  contents  of  surfaces  are  obtained  by  multiplying  the  length 
by  the  breadth,  and  that  the  quotient  of  the  contents  divided 
by  one  of  the  factors  gives  the  other. 

30.  I  want  a  piece  of  paper  to  cover  the  bottom  of  a  box 
that  is  two  inches  wide  and  four  and  one  half  inches  long  ; 
how  many  square  inches  must  it  contain  ? 

31.  The  leaves  of  my  book  contain  eight  square  inches  ; 
how  long  are  they  if  they  are  two  inches  wide  ? 


Suggestions  for  Teaching  Numbers.  1 2 1 


32.  I  have  a  little  cubical  box  whose  inside  is  one  inch  in 
length,  width,  and  depth  ;  how  many  half-inch  cubes  would 
fill  it  ?     How  many  inch  cubes  ?     Diagram. 

33.  How  many  inch  cubes  would  cover  the  bottom  of  a 
box  that  is  three  inches  long  and  two  inches  wide  ?     How 
many  inch  squares  would  cover  it  ?    How  can  you  ascertain 
without  trying  it  ? 

34.  How  could  you  find  the  number  of  square  inches  on 
the  cover  of  my  book  ?     You  may  do  it. 

35.  Mr.  Fox  hired  a  carriage  from  the  livery  stable  at  the 
rate  of  three  dollars  for  six  days  and  used  it  four  days; 
how  much  did  he  pay  for  the  use  of  it  ? 

36.  Dora  is  working  for  Mrs.  Wilson  for  a  dollar  and  a 
half  a  week  (of  seven  days);  how  much  will  she  receive  for 
four  weeks  and  three  and  a  half  days  ? 

37.  How  many  two-cent  pieces  would  you  give  me  for 
eight  cents  ?  for  seven  cents  ?  six  cents  ?  five  cents  ? 

38.  As  quickly  as  you  can,  give  me  the  results  of  the 
following  :  Five  less  three  ;  eight  less  five  ;  seven  less  four ; 
eight  less  two  ;  six  less  three  ;  nine  less  six  ;  nine  less  four; 
seven  less  two  ;   three  times  two  ;  two  times  four ;  three 
times  three ;    four  times  two  ;   eight  less  three  ;   five  and 
four  ;   two  and  six  ;   twos  in  four  ;  threes  in  six  ;  fours  in 
eight ;  twos  in  three  ;  threes  in  four  ;  threes  in  nine  ;  etc. 

39.  What  part  of  one  is  one  third  of  one  third.     Solu- 
tion : 

40.  What  part  of  one  is  one  half  of  one  fourth  :  Solu- 
tion : 


41.  What  part  of  one  is  one  fourth  of  one  half?     Solve 
by  diagram. 


Science  find  Art  of  Education. 


42.  One  eighth  is  what  part  of  one  fourth  ?     Solve  by 
diagram. 

43.  Two  eighths  equal  what  part  of  one  half.     Solve  by 
diagram. 

44.  Three  eighths  equal  what  part  of  five  eighths  ?  Solve 
by  diagram. 

45.  How   many   eighths   in   three   fourths  ?      Solve    by 
diagram. 

46.  How  many  eighths  in  two  thirds  ?    Solution  by  dia- 
gram. 

47.  How  many  thirds  in  five  eighths  ? 

48.  How  many  fifths  in  two  thirds.     Solution  : 


49.  How  many  fourths  in  three  fifths  ?    Solution  : 


50.  How  many  thirds  in  four  ninths  ? 

51.  How  many  halves  in  two  thirds  ?    Solution  : 


^*h 


52.  One  third  is  what  part  of  one  half? 

53.  How  many  eighths  in  one  fifth  ?    Solution : 

H 


J-K, 


Suggestions  for  Teaching  Numbers. 


54.  How  many  sevenths  in  one  sixth  ?     Solution: 


55.  One  eighth  is  what  part  of  one  third  ?    Solution  : 


K. 
56.  One  seventh  is  what  part  of  one  half?    Solution: 


Suggestive  Questions  and  Problems  on  Ten. 

1.  Three  threes  are  how  many  ones?     Add  one  to  them 
and  how  many  have  you  ?     (Nine  and  one  are  ten.) 

2.  Four  twos  and  two  ones  are  how  many  ones  ?  how 
many  twos  ? 

3.  Make  ten  of  fives  ;  how  many  does  it  take  ? 

4.  Two  fours  are  how  many  less  than  ten  ?  how  many 
more  than  six  ? 

5.  Six  and  how  many  make  ten  ?     Four  and  how  many 
make  ten  ? 

6.  How  many  threes  in  ten  ?     How  many  fours  ?     How 
many  sixes  ? 

7.  Seven  and  two  are  how  many  ?    How  many  more  than 
five  ?     How  many  less  than  ten  ?     How  many  more  than 
eight  ? 

8.  How  many  must  be  added  to  two  to  make  ten  ? 

9.  Make  ten  in  all  the  ways  you  can  mentally,  and   in 
each  case  state  the  result. 


124  Science  and  Art  of  Education. 

10.  What  is  one  half  of  ten  ?     One  fifth  of  ten  ?     Three 
fifths  of  ten  ? 

11.  To  one  third  of  nine  add  three  fourths  of  eight,  and 
what  is  the  sum  ? 

12.  What  is  the  sum  of  three  fourths  of  eight  and  two 
thirds  of  six  ? 

13.  What  is  the  sum  of  two  thirds  of  three  and  one  half 
of  nines  ? 

14.  Ten  less  seven  are  how  many  ? 

15.  How  many  fifths  of  five  must  be  added  to  five  sixths 
of  six  to  make,  nine  ? 

1 6.  I  know  a  number  which  doubled  makes  ten  ;  what  is 
it? 

17.  I  think  of  a  number  which  taken  three  times  and 
two  added  makes  eight ;  what  is  it  ? 

1 8.  What  number  diminished  by  its  third  leaves  six  ? 

19.  What  number  increased  by  its  half  equals  nine  ? 

20.  Six  times  a  number  diminished  by  five  equals  one; 
what  is  it  ? 

21.  The  sum  of  two  numbers  is  seven  and  one  of  them 
is  four,  what  is  the  other  ? 

22.  What  number  added  to  one  third  of  ten  makes  four  ? 

23.  If  you  double  a  number  and  take  four  from  it  you 
have  six  ;  what  is  the  number? 

24.  Ten  thirds  equal  how  many  ones  ? 

25.  How  many  ones  in  ten  fourths  ?  in  ten  fifths? 

26.  How  many  tenths  in  one  fifth  ?  in  one  half? 

27.  Two  fifths  and  one  half  equal  how  many  tenths?. 

28.  Can  you  malce  tenths  of  fourths  ?  Why  not  ? 

29.  What  can  you  make  of  halves  and  fourths  ?  Why  ?  o.f 
halves  and  thirds  ?  Why  ?  of  halves  and  fifths  ? 

30.  What   can  you  make  of  halves,  thirds,   and  sixes? 

Solution  by  diagram  : 

X 


Suggestions  for  Teaching  Numbers.  125 

31.  One  half  and  tsvo  thirds  equal  how  many  ones  ? 

32.  Can  you  add  halves,  fourths,  and  eighths  ?  How  ? 

33.  Can  .  you   add   halves   and  fifths  ?  How  ?  Show   by 
diagram. 


34.  In  a  piece  of  goods  ten  yards  long  and  one  yard 
wide  how  many  square  yards  ?    Prove  it. 

35.  How  many  yards  long  is  a  ten-foot  pole  ? 

36.  Helen's  apron  is  two  feet  in  length   and  a  half-yard 
in  width  ;  what  part  of  a  square  yard  of  goods  does  it  con- 
tain ? 

37.  A  board  eight  feet  long  contains  four  square  feet; 
how  wide  is  it  ?  What  would  its  width  be  if  it   contained 
ten  square  feet  ? 

38.  My  table  is  a  yard  in  length  and  five  sixths  of  a  yard 
in  width  ;  how  much  will  it  cost  to  cover  it  with  oilcloth 
at  six  tenths  of  a  dollar  a  square  yard  ? 

39.  How  would  you  find  the  number  of  square  feet  of 
paper  required  to  cover  the  lower  sash  of  that  window  ? 
Do  it. 

40.  Here  is  a  chest  that  is  four  feet  in  length,  two  feet 
in  width,  and  one  foot  in  depth  ;  how  many  blocks,  each 
containing  a  cubic  foot,  would  exactly  fill  it  ?     How  can 
you  tell  ?     Show  by  a  diagram. 

41.  Henry  bought  a  half-gallon  of  cherries  at  five  cents 
a  quart  and  paid  for  them  with  five-cent  pieces  ;  how  many 
did   it  take  ?  How  many  two-cent  pieces  would  pay  for 
them  ?     How  many  ten-cent  pieces  ?     How  many  dimes  ? 

42.  John  sold  nine  pigeons  at  the  rate  of  a  half-dollar  a 
pair  ;  how  much  did  he  receive  for  them  ?     How  many 
quarter-dollars  ? 

43.  When  sugar  is  five  cents  a  pound,  what  will  one  and 
cost  two  thirds  pounds  ? 

44.  Mr.  Down  loans  money  at  a  third  of  a  cent  on  a  dol- 


1 26  Science  'and  Art  of  Education. 

lar  a  month  ;  how  much  interest  does  he  receive  for  the 
use  of  five  dollars  for  three  and  a  half  months  ?  for  six 
months  ? 

45.  At  a  half-cent  a  month  on  a  dollar,  in  what  time 
would  six  dollars  give  nine  cents  interest  ? 

46.  At  a  fourth  of  a  cent  a  month,  how  many  dollars 
(how    much   principal)    would  in  four  months  give  eight 
and  three  fourths  cents  interest  ? 

47.  At  what  rate  (how  many  cents  on  the  dollar)  will 
four  dollars,  in  three  months,  give  six  cents  interest  ? 

48.  If  Henry  adds  the  interest  of  nine  dollars,  at  a  third 
of  a  cent  a  month,  for  two  and  a  half  months,  to  the  princi- 
pal, what  will  the  amount  (sum)  be  ? 

49.  If  five  oranges  cost  nine  cents,  what  is  the  cost  of 
three  of  them  ? 

50.  When  two  fifths  of  a  yard  of  tape  cost  four  cents, 
what  does  a  half-yard  cost  ? 

51.  Three  yards  of  lining  cost  nine  cents  ;  at  the  same 
price,  what  would  two  and  two  thirds  yards  cost  ? 

52.  At  two  thirds  of  a  cent  each,  how  many  oranges  can 
be  bought  with  two  cents  ?     Solution:  i.  If  they  had  cost 
one  third  of  a  cent  each,  for  two  cents  six  could  have  been 
bought ;  but  since  they  cost  two  thirds  of  a  cent  each,  only 
half   as   many  can   be   bought   as   if  they  cost  one   third 
of  a  cent  each,  or  three.     2.  Since  two  thirds  of  a  cent 
pay   for   one   orange,  one  third  of  a  cent  would  pay  for 
one  half  of  it,  three  thirds  for  three  halves,  and  two  cents 
for  two  times  three  halves,  which  are  six  halves,  or  three. 

53.  At  three  fourths  of   a  cent  each,  how  many  yards  of 
cord  could  you  buy  for  two  and  a  half  cents  ? 

54.  Mary  bought  six  dollars'  worth  of  cloth  at  two  and  a 
half  dollars  a  yard  ;  how  many  yards  did  she  buy  ? 

55.  In  ten  pecks  how  many  bushels  ?  In  nine  pecks  how 
many? 

56.  In  a  half-bushel  of  cherries,  how  many  gallons  ? 


Suggestions  for  Teaching  Numbers. 


127 


57.  One  is  what  part  of  ten  ?  of  nine  ?  of  seven  ?  of  two 
and  a  half  ? 

58.  Five  is  what  part  of  ten  ?  of  nine  ?  of  six  ? 

59.  What  part  of  one  is  one  third  of  one  third  ? 


NT1-.H. 
60.  What  part  of  one  is  one  fourth  of  one  half? 


6 1.  One  half  of  one  fifth  is  what  part  of  one  ?  Solve  by 
diagram. 


62.  How  many  fourths  in  two  thirds  ?      H( 


63.  How  many  ninths  in  one  half  ? 


-2%. 


64.  How  many  eighths  in  one  third  ? 


65.  One  fourth  is  what  part  of  one  third  ? 


66.  One  fifth  is  what  part  of  one  half  ?  of  one  third  ? 
Solve  by  diagram. 

67.  How  many  fifths  in  one  third  ?     Solve  by  diagram. 

68.  One  ninth  is  what  part  of  pne  third? 


128 


Science  and  Art  of  Education. 


69.  One  eighth  is  what  part  of  one  third  ? 


70.  One  fourth  is  what  part  of  two  sevenths  ? 


71.  One  half  is  what  part  of  three  fifths  ? 

72.  How  many  times  can  you  find  three  fourths  in  six  ? 


73.  How  many  times  can  you  find  two  thirds  in  five  ? 

74.  How   many   times   can   you   find  One  half  in  three 
fourths  ? 

75.  Two  thirds  are  what  part  of  four  ? 


76.  If  a  tailor  can  make  a  pair  of  pantaloons  in  a  day 
how  long  would  it  take  two  tailors  to  make  them  ? 

77.  Two  boys  can  pick  two  quarts  of  berries  in  an  hour  , 
how  long  would  it  take  one  of  them  to  pick  them  ?    How 
long  would  it  take  three  boys  to  do  it  ? 

78.  Four  boys  gathered  two  bushels  of  chestnuts  in  two 
hours  ;  how  many  boys   could,   in   the   same   time,    have 
gathered  three  bushels  ? 

79.  If  five  cows  can  eat  an  acre  of  grass  in  one  week, 
how   long  would  it  take  one  cow  to   do  it  ?     How   long 
would  it  take  one  cow  to  eat  two  acres  ? 

80.  Emma  can  make  a  dress  in  two  days  and  Jennie  in 
three  ;  what  part  of  it  can  each  make  in  a  day  ?     What 
part  of  it  could  the  two  together  make  in  a   day  ?     How 
long  would  it  take  them  to  make  it  working  together  ? 


Suggestions  for  Teaching  Numbers.  129 

81.  A  man  and  a  boy  together  do  a  piece  of  work  in  two 
days  ;  what  part  of  it  does  each  do,  if  the  man  does  twice 
as  much  as  the  boy  ?     How  long  would  it  take  each  alone 
to  do  it  ? 

82.  Bessie   and   Elsie  received   nine   cents   for   picking 
strawberries  ;  how  much  did  each  receive,  if  Elsie  received 
half  as  much  as  Bessie  ? 

83.  Henry  can  do  three  times  as  much  work  in  a  day  as 
Samuel  ;  how  long  would  it  take  Henry  to  do  what  Samuel 
can  do  in  two  days  ?    How  long  would  it  take  Samuel  to  do 
what  Henry  can  do  in  two  days  ? 

84.  Find  the  length  and  width  of  the  smallest  board  that 
you  could  exactly  cover  either  with  two-inch  or  three-inch 
squares. 

85.  What  is  the  smallest  bag  that  you  could  make  that 
could   be   exactly  filled   with    a  pint-measure   or  a  quart- 
measure  of  chestnuts  ? 

86.  What  is  the  length  of  the  shortest  pole  that  could  be 
exactly  measured  either  with  a  two-foot  measure  or  with  a 
yard-stick  ? 

87.  What  is  the  smallest  number  of  apples  that  you  could 
all  sell  either  by  twos  or  threes  ? 

88.  What  is  the   largest   measure  with  which    I    could 
empty  each  of  two  boxes,  one  containing  a  quart  of  berries, 
the  other  a  gallon  ? 

89.  Mr.  Miller  has  two  baskets  of  cherries,  one  contain- 
ing two  quarts,  the  other  three  ;  what  is  the  largest  cup 
with  which  he  can  exactly  measure  the  contents  of  each 
basket  ? 

90.  What  is  the  largest  measure  that  is  contained  in  three 
feet,  six  feet,  and  nine  feet  ?  in  four  feet  and  eight  feet  ? 
in  four  feet,  six  feet,  eight  feet,  and  ten  feet  ? 

I.  Writing  Numbers  aboiw  Nine. 

REMARK. — The  pupils  are  supposed  to  have  learned  to  write 
and  use  numbers  up  to  ten. 


130  Science  and  Art  of  Education. 

1.  They  should   now  be  told   that   nine  is   the   highest 
number  that  we  can  write  with  one  figure,  and  that  above 
nine  the  numbers  are  written  as  tens  and  ones. 

2.  Before   the    children   are   taught   to  write   ten,   they 
should  have  practice  in  finding  the  number  of  tens  in  a 
number   of   objects  ;    tying  toothpicks,    or   other   suitable 
objects,  into  bundles  of  tens,  affords  perhaps  the  best  prac- 
tice in  counting  by  tens.    One  bundle  should  be  called  one 
ten,  two  bundles  two  tens,  three  bundles  three  tens,  etc. 

3.  If  a  pupil  has  more  toothpicks  given  him  than  make 
an  exact  number  of  tens,  the  remainder  should  be  con- 
sidered as  so  many  ones  (or  units).     For  example,  if  he 
should  have  sixteen  given  him,  after  having  made  all  the 
possible  bundles,  he  would  have  six  toothpicks,  or  ones,  left. 

4.  To  make  the  bundles,  the  children  should  sit  or  stand 
around  a  table,  each  having  a  small  handful  of  splints  or 
toothpicks  before  it,  and  rubber  bands  or  threads  to  tie 
those  of  a  bundle  together. 

5.  After  the  bundles  have  been  made  the  children  should 
count  both  them  and  the  single  things  or  ones,  and  write 
the  results  in  columns  prepared  for  the  purpose.     After  each 
child  has  written  its  results  or  sums  in  the  proper  columns, 
the  columns  should  be  added,  also  the  bundles  and  single 
things,  and  the  results  compared. 

Example  i :  Suppose  there  are  four  children  and  each  has 
made  its  bundles  ;  the  first  having  2  bundles  and  4  single 
things  ;  the  second,  4  bundles  and  3  single  things  ;  the 
third,  i  bundle  and  7  single  things  ;  and  the  fourth,  i 
bundle  and  2  single  things.  They  now  write  Tens  o/i6« 
their  results  in  columns,  as  here  indicated,  and 
add  them.  The  first,  or  ones'  column,  gives  i 
bundle  and  6  single  things.  Writing  the  6  under 
the  ones'  column  and  adding  the  bundle  to  the 
tens,  gives  as  the  result  of  both,  9  bundles  and  6  single 
things, 


Suggestions  for  Teaching  Numbers.  131 

After  the  sums  of  the  columns  have  been  ascertained,  the 
children  should  give  their  bundles  and  remaining  tooth- 
picks to  one  of  their  number,  who,  after  having  made  as 
many  bundles  as  possible  of  the  remaining  single  tooth- 
picks, should  compare  her  bundles  and  remaining  toothpicks 
with  the  sums  of  the  columns. 

Example  2 :  REMARK. — This  example,  besides  carrying  the 
work  another  step  forward,  also  introduces  the  nought. 

Let  us  suppose  that  there  are  six  children  in  the  class, 
each  having  made  its  bundles  ;  the  first  having  3  bundles 
and  5  toothpicks  ;  the  second,  4  bundles  ;  the  third,  2 
bundles  and  7  toothpicks ;  the  fourth,  3 
bundles  ;  the  fifth,  2  bundles  and  8  tooth- 
picks, and  the  sixth,  2  bundles.  Adding  the 
columns  and  also  the  toothpicks,  it  is  found 
that  there  are  ten  bundles  and  eight  bundles; 
but  since  there  can  be  no  more  than  ten  of  a 
kind,  the  ten-bundles  must  be  tied  together, 
making  a  ten-ten  bundle,  and  its  number  written  at  the  foot 
of  a  line  next  to  the  left  of  the  tens. 

6.  The  children  should  work  with  toothpicks  in  connec- 
tion with  figures  until  they  can  write  and  read  numbers  to 
one  hundred  at  least.     They  should  also  be  led  to  see  that 
all  numbers  above  ten  are  composed  of  tens  or  tens  and  ones; 
and  instead  of  continuing  to  use  the  names  tens  and  ones,  the 
usual  names  should  gradually  be  introduced.    Thus,  for  ex- 
ample, instead  of  saying  one  ten  and  six,  two  tens  and  four, 
etc.,  they  should  learn  the  names  sixteen,  twenty-four,  etc. 

REMARK. — The  nought,  having  no  numerical  value,  is  used 
to  give  the  significant  figures  their  proper  places. 

7.  The  pupils  should  be  led  to  see  that  the  value  of  a 
figure  depends  upon  the  place  it  occupies  in  a  number  ; 
that,  in  general,  every  ten  of  one  place  makes  one  of  the 
next  to  the  left,  or  higher,  and  also  the  reverse,  namely,  that 
overy  place  to  the  right  is  one  tenth  of  the  next  to  the  left. 


1 3  2  Science  and  Art  of  Education. 

2.     Suggestions  on  Teaching  Numbers  up  to  Twenty. 

The  numbers  up  to  twenty  at  least  should  be  so  thorough- 
ly taught  that  the  pupils  can  instantly  give  the  sum  or  pro- 
duct (less  than  twenty)  of  any  two  of  them  ;  also  the 
reverse  ;  and  if  a  sum  or  product  is  given  and  one  of  the 
two  numbers  or  factors  that  compose  it,  the  other  should 
instantly  be  upon  the  pupils'  lips. 

3«  A  Device  for  Oral  Addition. 

Two  numbers  below  ten,  whose  sum  exceeds  ten,  may 
readily  be  added  by  taking  the  difference  between  the  larger 
and  ten  from  the  smaller,  adding  it  to  the  larger,  and  add- 
ing the  remainder  of  the  smaller  to  ten,  the  sum.  Example  : 
To  find  the  sum  of  6  and  8.  The  difference  between  8  and 
10  taken  from  6,  and  added  to  8,  makes  10;  and  4,  the  re- 
mainder of  the  smaller,  added  to  10,  makes  14. 

REMARK. — The  teacher  should  lead  the  children  to  discover 
every  device  that  will  enable  them  to  overcome  their  early 
difficulties  and  lighten  their  labor. 

4.  The  Four  Fundamental  Processes  Carried  on  Together. 
It  should  be  borne  in   mind  that  addition,  subtraction, 

multiplication,  and  division  are  to  be  carried  on  together. 

5.  Pupils  May  Construct  the  Tables. 

To  familiarize  themselves  with  the  relations  of  number, 
the  children  may  construct  the  tables,  but  in  giving  the 
results  in  class  they  must  not  think  of  the  position  of  the 
numbers  in  the  table,  but  must  give  them  instantly — as 
far  as  reasonable,  automatically. 

6.  Suggestive  Exercises  for  Seat  Work. 
REMARK. — o  =  what  ? 

I.  2.  3.  4. 

1.  1001  =  11  I.      0  +  2=12  I.      1+0=13  1.10  +  4=0 

2.  9  +  0=11  2.12—0=8  2.1301  =  12  2.1301  =  14 

3.  0—1  =  10        3.     0  +  3=12         3.  10  +  3=0          3.  14—0=9 

4.  8  +  3=0          4.  1202=10        4.  13—0=9          4.     04-2=7 

5.11-0=9        5.    0x3=12       5.   0+7=13       5.11+0=14 


Suggestions  for  Teaching  Numbers. 


'33 


6.        0-:-I  =  II 

7.  11—4=0 
8.    0  +  5  =  11 
9.    7+0=11 

10.      0  +  0=11 

n.    0—0=6 
etc. 

5. 

6.   12—7=0 
7.     705  =  12 
8.    0x0=12 
9.    0-0=7 

10.      O  +  O=I2 
II.       O-r-O  =  6 

etc. 

6. 

6.  13-5=0 
7.    0+0=13 
8.    0—0=3 
9.  13—8=0 
10.  1102=13 
n.  13—0=6 
etc. 

7. 

6.    7x2=0 
7.    608  =  14 
8.    0x0=14 
9.    0+0=14 
10.    0—0=5 

II.      0-r-0=2 

etc. 

8. 

i.    0+14=15 

i.    0+10=16 

i.  10+7  =o 

I.      0-1  =  17 

2.  15—0  =10 

2.  16—  o  =9 

2.     0—6    =11 

2.      I+0=l8 

3.    906  =15 

3.    0  +  3  =16 

3.  1708  =9 

3.    1803  =  15 

4.     5x0=15 

4.  16—  10=0 

4.  15+0  =17 

4.    15  +  3=0 

5.  15—10=0 

5.    0+11  =  16 

5.  17-3  =o 

5.      0-5  =  13 

6.  1503  =5 

6.  16013=3 

6.    0-14=3 

6.    6+0=18 

7.    o-i  =14 

7.    o+o  =16 

7.  17012=5 

7.  18-7=0 

8.    oxo  =15 

8.    oxo  =16 

8.    7+0  =17 

8.    0+0=18 

9.    o+o  =15 

9.    o-o  =5 

9.    0  +  9  =17 

9.    0x0=18 

10.      O-HO    =3 

10.     o-*-o  =4 

10.    o+o  =17 

10.    0—0=7 

ii.    o—  o  =4 

ii.     8  +  8  =o 

ii.    o—o  =6 

II.      0-5-0=2 

etc. 

etc. 

etc. 

etc. 

9. 

10. 

n. 

12. 

i.    0+3  =19 

i.  19+0  =20 

i.  £  of  4=0 

I.  i  Of  0    =f 

2.    I9  —  O    =15 

2.    20  —  3    =° 

2.   $  Of  8=0 

2.    2  X  O    =1 

3.  1  1  +8  =o 

3.    0  +  14=20 

3.  i  of  6=0 

3.  o  of  6  =4 

4.  1906  =13 

4.  20  o  11=9 

4.  £  of  9=0 

4.  0  X  f    =2 

5.    0+7  =19 

5.    3+0  =20 

5.  i  of  5=0 

5.  i  of  o  =| 

6.  19—0  =6 

6.    4+16=0 

6.  i  of  4=0 

6.  f  of  2  =o 

7.    3  +  16=0 

7.  20—8  =o 

7.  i  of  8=0 

7.  i  of  3  =0 

8.  1908  =11 

8.    0+6  =20 

8.  f  of  9=0 

8.  |  of  4  =0 

9.    0-14=5 

9.      0  +  0   =20 

9.  f  of  7=0 

9.  §  of  10=0 

10.     o+o  =19 

10.      0X0    =2O 

10.  $  of  4=» 

10.  f  Of  2    =O 

ii.    o—  o  =8 

ii.    O-HO  =5 

ii.  i  of  7=0 

ii.  £  of  6  =0 

etc. 

etc. 

13. 

14. 

15. 

16. 

i.  4  =  |  of  o 

i.  4  x  i=o 

i.    9=  f  of  o 

I.   |  Of  12=0 

2.  5  =  4  of  o 

2.  o  x  4=5 

2.    8=  $ofo 

2.  i  of  3  =0 

3.  6  =  \  of  o 

3.  i  of  0=3 

3.    3=  1  of  o 

3.  \  of  i£=o 

4-  ox  |  =  f 

4.  i  of  o=i 

4.    2=  5  x  o 

4.  £  of  o  =i 

1 34  Science  and  Art  of  Education. 


5.  f  of  o  =  3         5. 

O  X    £  =  2          5.    12=    f  Of  0         5.    0    X   $    =| 

6.  8  =  f  of  o        6. 

^  x  o=*      6.     |=  | 

of  o      6.  |  of  o  =7 

7.  9  =  1  of  o        7. 

f  ofo=f      7.     5=  3 

x  o      7-  i  of  o  =3* 

8.  2  =  f  of  o        8. 

o  x  2=3      8.    i=  i 

x  o      8.  i  of  2  =6 

9.  i  =  3  x  o        9. 

2    X   O=5         9.       I—  O 

=  i      9.  2  x  o  =i 

10.  6  =  f  of  o      10. 

|  of  5=0     10.    o  +  3f 

=  5£  10.  o  x  1^=4 

II.   f  —  i   Of  0         II. 

o  x  1=1     ii.    fos 

=  2     ii.  •}  of  o  =£ 

17. 

18. 

19. 

i.    Jofo  =  i 

i.    f  ofi  =0 

i.     5  =  f    of  o 

2.    If  X  0  =  4 

2.      fof     f=0 

2.      f  Of  2      =4X0 

3.      0  X  2  =  If 

3.    i  of    1=0 

3.     f  of  3    =3x0 

4.     f  of  0=14 

4.     |  of    4=1  of  o 

4.  18  =  i£  x    o 

5.     0-1-4  =  1 

5.    fof    5=2  x  o 

5.     2  x  o    =  £of  3 

6.   if  x  o  =  5 

6.  i£  x  2i=£of  o 

6.      $off    =   iofo 

7.     f  x  0  =  3 

7.     i=   fofo 

7.    IO  =  2      X     £ofo 

8.   \\  x  o=  i 

8.     i  of    1=0 

8.     f  =f    of  o 

9.  2*  x  o  =  \ 

9.    i=   fofo 

9.     fof£    =  fofo 

10.  3i  =  i  °f  ° 

10.       £  =     |  Of  0 

10.       i  Of  $    =  Tx¥  Of  0 

II.    2f   X  0  =  | 

ii.    f  =   i  of  o 

ii.   18  =41  x   o 

20. 

21. 

22. 

i.    9  =    9xf  of  o 

I.    12   -r-  0      =9 

i.     o  -4-  4f      =si 

2.      $  Of     2=f  Of  0 

2.      9  =  12    X    0 

2.     5  =  |      ofo 

3.  2f  x    0=18 

3.  10  =  f    of  o 

3.     f  of  o       =9 

4.    o  x    4=15 

4.  15  =  16  x  o 

4.    o  x  18      =17 

5.      f  Of     2=£     X  0 

5.    i  of  5    =10x0     5.   14  =  15      x   o 

6.    f  of    2=f  of  o 

6.    0x9    =6 

6.  15=1       of  o 

7.    I  of    f=fofo 

7.     5  -T-  o    =  20 

7.   13  =  f       of  o 

8.    f  of    ±=f  of  o 

8.    8-4-0    =  if 

8.     9x1^=0x2 

9.    f  of    4=16  xo 

9.      f  Of  0     =2 

9-  3f  -*-  1    =o 

10.  17  =  5f  xo 

10.    6xo    =  i| 

10.  4|  -5-  o        =3 

II.      ^   0      2  =  lf 

11        |    X  O     =  £ 

ii.     f  -*-  o        =  i 

23. 

24. 

25. 

I.        O-r-4    =  lf 

I.    0x18=19 

I.    2f     -4-0=f 

2.     3-0  =f 

2.    4-5-  0=  8 

2.      f    -4-0=  If 

3.     6  of  =4 

3-     5-*-  4=  ° 

3-     o  -f  =f 

4.       I  0  2    =f 

4.    0-5-  •$•=  6 

4.  if  +o=3f 

5.      f  02    =  lf 

5-    f  +  o=  1 

5.    2f    Xf=0 

6,      0-5-f    =1 

6.  13  x  0=17 

6.  1^x0=17 

Suggestions  for  Teaching  Numbers. 


135 


7.     f-J-o  =3                   ; 

8.      O-f    =2 

9.     ^xi  =o                  c 

10.    2i—  0    =  l£                      K 

ii.     o-*-4i=4i               ii 

26. 
I.     o—  lf=2|             Lem 
2.    12-5-0    =3| 
3.      0  Of  Ii=2 

4.    3  -5-  o  =8 
5.    4-5-0  =3 
6.    9  x  o  =19 

r.    12-1-   O=    9 
).      9=   OX  12 

:>.  15-5-  0=20 
.     o-f-  |=I5 

27. 

ons.  cts.  Lemons. 

2           3 

3        2 

I           4 
4           3 

2        4 

7-    f  oi=3 
8.    f  =5x0 

9.   2|    X2=f   Of  0 

ii.  ii  +o=3i 

28. 

Oranges  cts.  Oranges. 

4        5 

2        7 

3        5 
6        3 
7        2 

7- 

0 

x  17  =  13 

5 

3 

3 

6 

2 

8 

7 

-h-  0 

=  12 

2 

6 

4 

8 

3 

9- 

1  1 

X  0 

=  16 

6 

2 

5 

15 

2 

10 

12 

—  0 

=8* 

4 

4 

2 

4 

3 

u. 

fof* 

=0 

5 

2 

3 

9 

4 

2 

6 

3 

29. 

30. 

31. 

Apples. 

cts. 

Apples.                Yds. 

cts. 

Yds. 

Yds. 

cts. 

Yds. 

3 

12 

4                 4 

12 

6 

I 

15 

^ 

4 

16 

3                  6 

12 

9 

f 

3 

2i 

2 

IO 

4                 8 

16 

i 

I| 

2 

3 

5 

15 

4                 5 

15 

i 

2i 

4 

1 

2 

4 

8                        2 

16 

i 

f 

ii 

f 

7 

7 

5                   i 

2 

3 

f 

ii 

2i 

4 

20 

3                 i 

2 

i 

1 

JT 

4 

6 

12 

7                  i 

2* 

4 

2 

2i 

f 

7 

H 

9                 * 

8 

| 

| 

2 

t 

9 

18 

8                 f 

9 

I 

| 

f 

2i 

8 

16 

7                 2 

16 

1 

Ii 

2± 

2* 

REMARK.—  To  indicate  how  the  exercises  under  27-31  should 
be  read,  the  first  under  29  may  be  taken  as  an  example.  If  3 
apples  cost  12  cents,  what  cost  4  apples  ? 

7.       Suggestive  Problems  for  Oral  and  Seat  Work. 

1.  If*  4  quarts  of   milk  cost  8  cents,  what  will  8£  quarts 
cost? 

2.  If  2^  yards  of  tape  cost  15  cents,  what  will  if  yards 


DIVERSITY) 

v  o,n  ,<*„*.  y 


136  Science  and  Art  of  Education. 

3.  My  table  is  3^  feet  in  length  and  two  feet  in  width  ; 
how  many  square  feet  of  oilcloth  will  cover  it  ? 

4.  A  piece  of  cloth  is  one  yard  in  length  and  the  sajme 
in  width  ;  how  many  square  feet  of  paper  would  cover  it  ? 
How  many  square  feet  does  it  contain  ? 

5.  How  many  square  feet  in  a  surface  a  foot  square  ?  in 
one  a  yard   square  ?     in  one  3  feet  square  ?  in  one  4  feet 
square  ? 

6.  How  many  square  yards  in  a  surface  6  feet  long  and 
3  feet  wide  ? 

7.  I  have  a  box  that  is  2  feet  in  length,  i  foot  in  width, 
and  i-|  feet  in  height  ;  how  many  square  yards  of  paper 
would  cover  it  ? 

8.  Show  me  an  inch  on  this  foot-measure.     How  many 
inches  in  length  is  the  whole  measure  ?     How  many  inches 
are  in  a  foot  ?  in  a  \  foot  ?  in  f  of  a  foot  ?  in  f  of  a  foot  ?  in 
|  of  a  foot  ?  in  i£  feet  ?  in  i£  feet  ? 

9.  How  many  feet  in  9  inches  ?  in  8  inches  ?  in  14  inches  ? 
in  18  inches?  in  3  inches? 

10.  How  many  quarts  in  2  pecks  ?  in  a  half-bushel  ? 

11.  How  many  pecks  in   12  quarts?  in  18  quarts?  in  6 
quarts  ? 

12.  At  8  cents  a  gallon  what  would  12  quarts  of  milk  cost  ? 
What  would  18  quarts  cost? 

13.  Take  the  weights   and   find  out   how  many  ounces 
make  a  pound  (avoirdupois).    How  many  ounce  weights  are 
as  heavy  as  f  of  a  pound  ?     What  part  of  a  pound  weighs 
as  much  as  12  ounces  ? 

14.  How  could  you  add  into  one  sum  2^  feet  and  4  inches? 
How  5  feet,  f  of  a  foot,  and  8  inches  ?     How  3  yards,  2§ 
feet  and  18  inches  ? 

15.  Take  the  yard-stick  and  measure  5-}  yards  from  the 
platform  through  the  middle  of  this  aisle.     How  many  feet 
did  you  measure  ?    5^  yards,  or  i6j  feet,  are  called  a  rod. 

16.  How  many  rods  in  the  length  of  this  room  ?     How 


Suggestions  for  Teaching  Numbers.  137 

many  in  the  width  ?     How  many  feet  in  a  |  rod  ?  in  \  of 
a  rod  ?  in  f  of  a  rod  ? 

REMARK. — The  pupils  should  make  inch,  foot,  yard, -and  rod 
measures  and  use  them  in  measuring  lengths  and  distances. 
The  shorter  measures  may  be  made  of  wood,  the  longer  of  twine 
or  cord. 

17.  Add  into  one   sum  i    rod,  i£  yards,  i    foot,  and  8 
inches  ? 

1 8.  Find  the  sum  of  3  gallons,  2  quarts,  and  i  pint. 

19.  Find  the  sum  of  J  of  a  pound  and  7!  ounces. 

20.  How  many  pints  in  f  of  a  peck,  3^  quarts,  and  f  of 
a  pint  ? 

21.  How  many  feet  in  £  of  a  rod,  2^  yards,  2  feet,  and  9 
inches  ? 

22.  How  many  ounces  in  f  of  a  pound  and  2\  ounces  ? 

23.  In   15   pints  how  many  gallons  ?     One  pint  is  what 
part  of  a  gallon  ?   of  3  quarts  ?     Three  quarts  are  what 
part  of  three  gallons  ? 

24.  In  18  inches  how  many  feet?     What  part  of  a  yard  ? 

25.  Nineteen  ounces  equal  how  many  pounds  ? 

26.  Twelve  ounces  equal  what  part  of  a  pound  ? 

27.  In  17  feet  how  many  yards  ?  how  many  rods  ? 

28.  How  many  feet  in  16  inches  ?  in  10  inches  ? 

29.  In  15  weeks  how  many  months  ?  in  17  weeks  ? 

30.  How  many  weeks  in  2^  months  ?  in  £  of  a  month  ? 

31.  How  many  days  in  2^  weeks  ?  in  f  of  a  week  ? 

32.  In   14   quarts    how   many    pecks  ?    what   part   of  a 
bushel  ? 

33.  In  20  pints  how  many  pecks  ?  what  part  of  a  bushel  ? 
how  many  half-bushels  ? 

34.  How  many  months  in  \\  years  ?  in  if  years  ?  in  f 
of  a  year  ? 

35.  How  many  years  in  15  months  ?  in  8  months  ?  in  9 
months  ? 

36.  Find  the  interest  of  $2-£  at  6  per  cent  (6c.  on  a  dollar 


Science  and  Art  of  Education. 


for  a  month)    for  f  of   a    year?    for    16    months?   for   3 
months  ? 

37.  What  is  the  interest  of  $4!  at  3  per  cent  for  if  years  ? 
for  4  months  ? 

38.  The  interest  of  $5   for  2  years  is  2oc.  ;  what  is  it  of 
$i  for  i  year? 

39.  What  principal,  at  2C.  on  a  dollar  a  year,  will  in  16 
months  give  i5c.  interest  ? 

40.  In  what  time  (how  many  years)  will  $6,  at  2^  per 
cent,  give  i8c.  interest  ? 

41.  If  by  selling  my  knife  for  i6c.   I  gain  £  of  the  cost, 
what  was  the  cost  ? 

42.  Sarah  lost  \  of  its  cost  by  selling  her  bird  for  i2c.; 
how  much  had  she  paid  for  it  ? 

43.  By  selling  a  book  for  ice.  I  lost  J  of  its  cost  ;  what 
should  I  have  sold  it  for  to  have  gained  \  of  its  cost  ? 

44.  One  of  two  boys  can  do  a  piece  of  work  in  3  days, 
the  other  in  4  days  ;  what  part  of  it  can  each  do  in  a  day  ? 
What  part  can  both  together  do  in  a  day  ?    How  long  would 
it  take  both  together  to  do  the  whole  of  it  ? 

45.  If  it  takes  A  2  days  to  do  a  piece  of  work  and  B  5 
days,  how  many  days  would  it  take  them  together  to  do  it  ? 

46.  Four  men  can  do  a  piece  of  work  in  2  days  ;  how  long 
would  it  take  one  of  them   alone   to   do   it  ?     Solution  : 
oo  +  oo  +  oo  +  oo  =  8.     Let    every    o  represent    a   day's 
work  of  "each  man  ;  then  all  of  them  will  represent  8  days' 
work  of  a  man. 

47.  If  5  girls  can  make  a  certain  number  of  dresses  in  4 
days,  in  how  many  days  could  two  of   them  do  the  same 
work  ?     Illustrate  by  diagram  or  other  form. 

48.  If  5  boys  can  pick  30  bushels  of  apples  in  a  day,  how 
long  would  it  take   i   boy  to  do   it  ?     How  long  would  it 
require  3  boys  to  do  it  ? 

49.  If  10  is  f  of  a  number,  what  are  £  of  it  ? 


Suggestions  for  Teaching  Numbers.  139 

50.  If  f  of  Henry's  ducks  equal  -J  of  his  turkeys,  and  he 
has  24  ducks,  what  is  the  number  of  his  turkeys  ? 

51.  A  watch  and  chain  cost  $15  ;  what  was  the  cost  of 
each,  provided  the  chain  cost  f  as  much  as  the  watch  ? 

52.  If  Jennie  adds  8  years  to  £  of  her  age,  the  sum  will 
be  her  age  ;  how  old  is  she  ? 

53.  One  half,  £,  and  i  of  a  certain  number  added  to  8 
make  21  ;  what  is  the  number  ? 

54.  At  f  of  a  cent  each,  how  many  lemons  can  be  bought 
for  4  cents  ? 

55.  Alberta  bought  4  oranges  for  3  cents  ;  what  was  the 
cost  of  each  ?     How  many  did  she  get  for  i  cent  ? 

56.  At  $f  a  yard,  how  many  yards  of  cloth  can  be  bought 
for  $6  ? 

57.  A  boy  gave  $3  to  a  number  of  beggars,  giving  to  each 
$f  ;  how  many  beggars  were  there  ? 

58.  If  to  Alfred's  money  you  add  4  times  his  money,  he 
will  have  25c.;  how  much  money  has  he  ? 

59.  Find  the   difference   between  a  square  inch  and  an 
inch  square  ;  between  2  square  inches  and  2  inches  square. 

60.  What  is  the  difference  between  a   foot   square  and  a 
half-foot  square  ?     Illustrate  with  diagram. 

61.  How  many  6-inch  cubes  could  you  make  of  a  cubic 
foot  ?  how  many  4-inch  cubes  ?     How  many  2-inch  cubes 
could  you  make  of  a  6-inch  cube  ?     Diagram. 

62.  How  many  cubic  feet  in  a  box  that  is  3  feet  long,  2 
feet  wide,  and  i  foot  deep  ? 

63.  Could  you   find  how  many  square  yards  of  carpet 
would  cover  this  floor  ?     How  would  you  do  it  ?     If  the 
carpet  were  f  of  a  yard  in  width,  could  you  find  how  long 
a  piece  it  would  require  to  coyer  the  floor  ?    Illustrate  with 
diagram. 

64.  How  could  you  find  the  number  of  square  feet  of 
paper  required  to  cover  the  walls  and  ceiling  of  this  room  ? 
Could  you  find  the  number  of  square  yards  ?    How  ?  Could 


140 


Science  and  Art  of  Education. 


you  find  how  long  a  roll  it  would  require  if  the  paper  were 
only  a  half-yard  in  width  ? 

65.  How  many  foot  cubes  would  cover  the  floor  of  this 
room  ?  how  many  would  fill  the  room  ?  How  many  cubic 
feet  in  this  room  ?  how  many  cubic  yards  ? 

8.  Diagrams  and  Figures. 

1.  The  teacher  should  be  careful  that  pupils  do  not  mis- 
take fractional  expressions  for  fractions  ;  fractions  are  parts 
of  things  or  wholes,  and  fractional  expressions,  as  £,  £,  etc., 
are  the  signs  or  language  by  means  of  which  they  are  repre- 
sented. 

2.  Fractions   may   be   introduced   and   to   some   extent 
taught  by  means  of  folding  paper  01  by  various  forms  of 
diagrams.     The  following  illustrations,  in  addition  to  those 
already  given,  may  prove  helpful  to  teachers,  and  may  be 
preferred  by  some. 


X 

X 

XX 

g 

X 

3.  After  pupils  have  learned  to  work  with  real  fractions 
(parts  of  objects)  they  should  be  taught  the  signs  by  which 
they  are  represented. 

9.  Adding,  Subtracting,  Multiplying,  and  Dividing  by 
Diagrams. 

i.  How  many  fourths  in  -J  ?  in  £  and  \  ?     What       H 
part   of   one  is  |  of   4?  i  +  i=?  t+t=?  i  + 
i  =?  i+i  +  =?  i-i  =?*-*-*=?  etc. 


2.  How  many  sixths  in  one  ?  in  £  ?  in  \  ?     What  part  of 


Suggestions  for  Teaching  Numbers. 


141 


i  is  i  of  ^  ?  £  of  J  ?  k  is  what  part  of  -J  ?  £  is 
what  part  of  £?  i  is  what  part  of  £?  How  many 
sixths  in  £  ?  How  many  |  in  f  ?  How  many 


}(> 


-i=?i+i-H=?i  +  f=?   . 

Si    — ?   5  1    — >4         JL  — •>  _L    •     1   — ">  JL     •     1    - 

~~  6   —  •    1>  3   —  '3          2   —  •    *  ~  "6  —  •    2  ~  "5  ' 

3.  How  many  -J  in  i  ?  in  i  ?  in  -£  ?  ^  is  what 
i  of  |  ?  -J  of  J  ?     How  many  i  in  f  ?     How 
many  -J  in  §  ?     What  part  of  i  is  J  of  J  ?  £  of 
i  ?     How  many  i  in  $  ?     How  many  times  are 
f  contained  in  |?  -£-{-£=?  i  +  i=?  f  +  i 

=?  i  +  ±  +  i=.>  i  +  |=?  i-i=?  i-t 

=  ?  i  ^.  |  =?  i  -f-  f  =?  i  -f-  i  =?  etc. 

4-  i  of  i  is  what  part  of  i  ?  How  many 
is  what  part  of  £  ?  how  many  ^  in  i  ?  i  con- 
tains how  many  i  ?  how  many  i  in  f  ?  J  -f  •£  =? 

t  +  i  =? i-i  =?f-i  =?*  +  *=?  i -i-t 

=  ?  etc. 

5.  i  of  i  is  what  part  of  i  ?  How  many 
\  in  i  ?  How  many  ^  in  -J  ?  how  many  ^ 
^  ?  £  is  what  part  of  £  ?  ^V  is  what  part  of  £  ? 
How  many  ^  in  J  ?  How  many  £  in  J  ?  How 
many  times  is  £  contained  In  -^  ?  How  many 
times  are  ^  contained  in  4-  ?  -ft-  are  what  part 

ofm-ff  +  iV=?i-H=?i-|=?A- 


in 
in 


?  how  many 
U     H 


7.  What    is   i  of  }  ?  J  of  ^  ?  J  of  J  ?  How  many  ,1.>  in 


I42 


Science  and  Art  of  Education. 


\  ?  in  \  ?  in  J  ?  in  J  ?  How  many  \  in  £  ? 
in  i  ?    How  many  J  in  -£  ?  J  is  what  part       / 
of  4  ?  -J  is  what  part  of  \  ?  £  is  what  part  ^( 
of  f  ?    How  many^  in  f  ?  i  is  what  part       \ 
of  \  ?  How  many  J  in  f  ?  How  many  ^  in 
\  ?  f  equal  what  part  of  jj  ?  -J-  -j-  J  -j-^ 

M 

£ 

% 

% 

& 

fcfc 

£ 

K2 

K2 

K2 

^2K, 

t  -  A  =?  t  x  i  =?  i  x  i  =?  *  x  t  =?  f-x-t  =??  f  4-.i 

8.  How  many  ^  in  ^  ?    How  many  )&       *£ 

i  in  J  ?  ^  is  what  part  of  \  ?  -J  is  what      , . I^nT7T77h7T\ 

r     1    -i     1        il        i       li        1  •>       K        i  M    716    TIC     716    716        \ 

part  of  ^  ?  -|-  -J-  ^  +  ^  -f"  'iV  —  •   A  ~r  : ^ ) 

-A=?    lT^i=     f?     -5-f=?    t^A=?i         M    H6_K6_K6_^ 

X  i=?   ^Xi=?iXi=?fX2=:?     MJ^JM^J^ 
|Xi=?  i  X  TV  =?  etc. 

9.  What  is  i  of  I  ?  i  of  i  ?  i  of  i  ?  I  of  i  ?  i  +  I  +  i  =? 


Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

10.  One  fourth  is  what  part  of  i  ?  - 


wnat  part  of 


is  what  part  of  J  ?  of 
is  what  part  of^?  of^ 

=?ix  J=?t  xi=? 
4x^=?  jxf  =?A 


=? 


Ms 

Ms 

'  ;,. 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

to 

Ms 

Ms 

Ms 

to 

Ms 

Ms 

Ms 

Ms 

Ms 

Ms 

to 

to 

Ms 

Ms 

Ms 

to 

to 

to 

Ms 

Ms 

to 

to 

to 

to 

Ms 

Ms 

Ms 

to 

to 

to 

to 

Ms 

Ms 

to 

to 

Ks 

to 

Suggestions  for  Teaching  Numbers. 


ii.  How  many  .01  in  i  ?   How  many  .1  in  ^?  in 
many   .01  in  i  ?  in  i  ?     How 
many  .1  in  .50  ?  i  +  .1  +  .01 


?   How 


.1  .1  .1  .1  .1  .1  .1  .1  .1  .1 

Ho 

Mo 
Ka 
K« 
Hi 
Ko 
Ki 
Ko 
Ko 
Ko 

.01  .01 

(11 

01 

.01 

01 

.01 

01 

.01 

01 

.01  .01 

01 

01 

.01 

01 

.01 

01 

.01 

.01 

.01  .01 

.01 

01 

.01 

.01 

.01 

01 

.01 

.01 

.01  .01 

.01 

01 

.01 

.01 

.01 

.01 

.01 

.01 

.01.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01.01 

.01 

.01 

.01 

.01 

.01 

01 

.01 

.01 

.01.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01  .01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01  .01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01  .01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

.01 

-f  .05  =?   .56  —  .4  =? 


X  .10  =  ?T*TF  +  -3  =?.i+.i 

=  ?.!-.  01=?.!  +  ^=?  .1 
-T-.OI  =?t  -5--^=?  .01  +  .4 
=  ?.4  +  .07  =?.I2  +  T*ir=? 

.7  +  .6  -?  .18  +  .24  =?  .06  -4- 

.02  =?    .50  -f-  .05  =?    .75  -i-   .3  =? 

.09  —  .5  =?  .12^  -|-  .14  =?  etc. 

REMARK.—  If  the  foregoing  work  has  been  well  done,  the 
pupils  will,  to  such  an  extent,  have  learned  to  make  their  own 
discoveries  —  to  help  themselves  —  that  they  will  experience 
comparatively  little  difficulty  with  the  higher  numbers  and 
their  combinations. 

10.      Me,  tal  Addition  of  Two-figured  Numbers. 

1.  Two  numbers,  each  composed  of  tens  and  units,  may 
readily  be  added  mentally  by  first  finding  the  sum  of  the 
tens  and  then  adding  to  it  that  of  the  units.     Example  : 
Find  the  sum  of  28  and  39.     Two  tens  and  three  tens  are 
five  tons,  or  fifty,   and  8  units  and  9  units,  or  17  units, 
(added)  equal  sixty-seven. 

2.  As  soon  as  the  pupils  are  far  enough  advanced  to  do 
so,  instead  of  saying  two  tens  and  three  tens  are  five  tens, 
they   should   say  twenty   and  thirty  are  fifty,  etc.     They 
should  also  be  led  to  see  that  the  same  combination  of 
units   will   invariably   give   the   same   units'   figure.      For 
example,  6  and  7,  16  and  17,  26  and  37,  and  so  on,  will  all 
have  3  for  the  units'  figure. 

1  1  •  Subtracting  a  Greater  from  a  Less. 

i.  Subtracting  one  number  from  another  when  some  of 
the  figures  of  the  minuend  are  smaller  than  those  of  the 


T44  Science  and  Art  of  Education. 

subtrahend  to  be  taken  from  them,  may  be  developed  by 

453 

means  of  tooth-picks.     Example  :  — .     Since  4  cannot 

219 

be  taken  from  3,  one  of  the  ten-bundles  must  be  opened, 
its  contents  put  to  the  3  ones  and  the  4  taken  from  the 
sum. 

2.  The  same  thing  may  also  be  developed  with  dollars, 
dimes,    and    cents  of   toy-money.     Taking   the   foregoing 
example,  since  4  cents  cannot  be  taken  from  3  cents,  one 
of  the  ten-cent  pieces  of  the  minuend. must  be  exchanged 
for  cents  and  the  latter  added  to  the  three  to  make  the 
subtraction  possible.     One   ten   having   thus   been    taken 
from  the  5  of  the  minuend,  4  remain,  from  which  the  3  of 
the  subtrahend  must  be  taken. 

3.  The  teacher  should  lead  his  pupils  to  see  that  finding 
the  difference  between  two  numbers  is  the  same  as  finding 
what  must  be  added  to  the  smaller  to  make  the  larger,  and 
that  the  difference  may  therefore  be  found  either  by  addi- 
tion or  subtraction. 

4.  Methods  of  proof  should  also  be  developed,  so  that 
the  pupils  may  have  the  means  of  testing  the  correctness 
of  their  work. 

REMARK. — i.  As  far  as  possible  and  as  long  as  necessary  the 
solution  of  every  problem  should  be  illustrated  either  with 
objects,  diagrams,  or  drawings.  The  drawings,  at  first  crude, 
will  with  the  teacher's  assistance  gradually  improve  and  will 
create  an  interest  in  that  kind  of  work. 

REMARK. — 2.  It  cannot  be  too  strongly  impressed  upon  the 
mind  of  the  teacher  that  a  part  of  every  lesson  should  be  a 
review  of  some  of  the  previously  prepared  lessons  or  subjects 
passed  over.  Daily  reviews  give  not  only  clearness  to  concepts, 
but  impress  them  firmly  upon  the  mind. 

12.  Mental  Multiplication. 

i.  Mentally  finding  the  product  of  any  two  numbers  up 
to  100,  besides  affording  a  good  exercise  for  the  memory, 
enables  the  pupils  to  perform  many  arithmetical  operations 


Suggestions  for  Teaching  Numbers.  145 

without  resorting  to  pencil  and  paper.  To  illustrate  the 
method  of  doing  this  when  both  factors  are  less  than  20,  let 
it  be  required  to  obtain  the  product  of  14  by  14.  Fourteen 
is  the  sum  of  10  and  4.  First,  multiply  14,  the  multipli- 
cand, by  the  10  of  the  multiplier  (or  simply  annex  a 
nought);  next  the  10  of  the  multiplicand  by  the  4  of  the  mul- 
tiplier ;  add  the  two  products  ;  finally,  multiply  the  4  of  the 
multiplicand  by  the  4  of  the  multiplier  and  add  the  prod- 
uct to  the  sum  of  the  previous  products.  Operation : 
14  X  10  =  140  ;  10  X  4  =  40  ;  140  +  40  =  180  54X4 
=  16  ;  180  -f-  16  =  196. 

2.  The  foregoing  method  applies  as  well  to  unequal  as  to 
equal  factors.     For  example,  let  it  be  required  to  find  the 
product  of  19  by  15.     Operation  :    19  X  10  =  190  :   10  X 
5  =  50 ;  190  +  50  =  240  ;  9  X  5  =  45  ;  240  -f-  45  =  285. 

3.  To   find   the   product   of    any  two   factors   that  are 
greater  than  20  and  less  100,  multiply  the  multiplicand  by 
10,  the  product  by  the  number  of  tens  in  the  tens  of  the 
multiplier,  the  tens  of  the  multiplicand  by  the  units  of  the 
multiplier;   add  product  to  preceding  produt;  multiply  the 
units  of  the  multiplicand  by  the  units  of  the  multiplier,  and 
add  product  to  preceding  sum  of  products.     For  example, 
multiply  48  by  36.     Operation  :  48  X   10  =  480  ;  480  X  3 
=  400  X  3  -f-  80  X  3  =  1440  ;  40  X  6  =  240  ;   1440  -f-  200 
+  40  =  1680  ;  8  X  6  =  48  ;  1680  -f  40  +  8  =  1728. 

REMARK.-  As  an  aid  to  memory,  whenever  it  is  possible, 
round  numbers  (as  in  the  foregoing  operation)  should  be  mul- 
tiplied and  added. 

13-       Properties  of  Nine  and  Their  Application. 

1.  If  a  number  is  divisible  by  9  the  sum  of  its  figures  is 
divisible  by  nine.     Illustrative  examples  :    18,  27,  63,  81, 
4896,  etc. 

2.  The  remainder,  or  excess,  of  the  division  of  a  number 
by  9  is  the  same  as  that  of  the  sum  of  its  figures  divided 
by  9.     Illustrative  example  :  5843  divided  by  9  leaves  2  as 


146  Science  and  Art  of  Education. 

the  excess,  and  20,  the  sum  of  its  figures  (5  +  8  +  4  +  3), 
divided  by  9,  leaves  the  same. 

3.  The  excess  of  the  division  of  the  sum  of  two  or  more 
numbers  by  9  is  the  same  as  that  of  the  excess  of  the  sum 
of  their  excesses. 

From  this  fact  is  derived  one  of  the  simplest  and  quick- 
est methods  of  proving  addition  and  subtraction. 

4.  Application  to  Addition. — RULE  :    Find  the  excess  of 
each  of  the  numbers  added,  add  these  excesses,  find  the  ex- 
cess of  their  sum,  and  if  the  latter  is  the  same  as  the  excess 
of  the  sum  of  the  numbers  added,  the  work  may  be  con- 
sidered correct.     Illustrative  example  : 

5873 5,  excess  of  division  by  9. 

4652...... 8, 

8763 6, 

579 3^       "  "        " 

19867... 4.       22....  4. 

The  sum  (22)  of  the  excesses,  divided  by  9,  leaves  4  as 
the  excess ;  and  the  sum  (19867)  of  the  numbers  divided 
by  9  leaves  4,  the  same  excess. 

5.  Application  to  Subtraction. — RULE  :  Find  the  excess  of 
the   minuend,   subtrahend,  and   remainder    or   difference, 
add  those  of  the  remainder  and  of  the  subtrahend,  and  if 
their  sum,  or  the  excess  of  their  sum,  is  the  same  as  that  of 
the  minuend,  the  work  may  be  considered  correct.     Illus- 
trative example : 

8975 2,  excess. 

7487....^      " 

1488         3,        " 

Adding  (3)  the  excess  of  the  remainder  and  (8)  that  of 
the  subtrahend  and  dividing  the  sum  by  nine,  the  excess 
found  is  2,  the  same  as  that  of  the  minuend. 

NOTE. — The  excess  of  the  division  of  the  product  of  two  or 
more  factors  by  9  is  the  same  as  the  excess  of  the  product  of 
the  excesses  of  the  factors. 


Suggestions  for  Teaching  Numbers.  \  4  7 

From  this  fact  is  derived  one  of  the  simplest  and  most 
expeditious  modes  of  proving  multiplication  and  division. 

6.  Application  to  Multiplication.  —  RULE  :  Find  the  excess 
of  the  product  and  of  each  of  the  factors,  multiply  that  of 
the  multiplicand  (or  the  reverse)  by  that  of  the  multiplier, 
find  the  excess  of  their  product,  and  if  it  is  the  same  as 
that  of  the  product  of  the  factors,  the  work  may  be  re- 
garded as  correct.  Illustrative  example  : 


687.  . 


4IIH        !$••••  «6 
46984 
35238 

4Q34751 6 

The  excess  of  the  product  (4034751)  is  6,  that  of  the 
multiplicand  (5873)  5,  and  that  of  the  multiplier  3  ;  and 
the  excess  of  the  product  (15)  of  the  latter  two  is  6,  the 
same  as  that  of  the  product  of  the  factors. 

7.  Application  to  Division. — RULE:  Find  the  product  of 
the  excess  of  the  divisor  and  of  that  of  the  quotient ;  to  it 
add  the  remainder,  or  its  excess  (if  it  has  one)  ;  and  if  the 
excess  of  the  sum  is  the  same  as  that  of  the  dividend,  the 
quotient  may  be  considered  correct.    Illustrative  example  : 
26)  6547  (251 
52 


130 

47 
26 


The  excess  of  9*5  of  the  divisor  (26)  is  8,  that  of  the 


148  Science  and  Art  of  Education. 

quotient  (251),  8,  their  product  is  64  ;  to  this  add  (3)  the  ex- 
cess of  the  remainder  (21),  and  the  excess  of  the  sum  (67) 
is  4,  the  same  as  that  of  the  dividend. 

NOTE. — The  only  case  in  which  the  foregoing  proofs  could 
fail  would  be  when  one  error  would  balance  another — when, 
for  instance,  56  would  be  written  65,  or  o  written  instead  of 
9;  but  since  such  errors  are  of  the  rarest  occurrence,  the  proof 
by  the  rejection  of  the  9's  may  be  considered  of  equal  validity 
with  any  others. 

14*  Composition  of  Numbers. 

1.  The  pupils  should  be  led  to  see  how  numbers  are  com- 
posed.    The  following  may  serve  to  show  how  it  may  be 
done : 

78964  =  70000  -f-  8000  -j-  900  -f-  60  -f~  4. 
9000  -J-  700  +  80  +  3  =  9783. 

2.  The  numbers  may  also  be  written  in  vertical  columns  : 

78964  9000 

700 

70000  80 

8000  3 

900 
60  9783 

4 
15.  Some  Points  in  Multiplication. 

1.  When  the  multiplicand  coiioists  of  several  figures  and 
the  multiplier  of  but  one,  the  pupils  are  usually  instructed 
to   begin   at  the  units'   place   of  the   multiplicand   and   to 
multiply  each  of  its  figures  in  succession  by  the  multiplier ; 
but  this  procedure  is  looked  upon  by  the  pupils  as  arbi- 
trary.    If,  however,  taking  the  following  example,  456  X  8, 
the-  multiplicand   be   separated   into   400,  50,  and  6,  and 
the  pupils  told  to  find  the  sum  of  the  products  of  these 
numbers  each  multiplied  by  8,   and   then  be   led   to   see 
that  the  usual  method  is  an  abbreviation  of  this,  all  thought 
of  arbitrariness  will  disappear. 

2.  A  development  of    multiplication  like  the  following 
throws  light  upon  points  frequently  not  well  understood : 


Suggestions  for  Teaching  Numbers.  149 

456  X  234  —  400  X  200  -|-  400  X  30  +  400  X  4  +  5° 
X  200  -f  50  X  30  +  50  X  4  -f  6  X  200  +  6  X  30  +  6 
X  4  = 

400  X  200  =   80OOO 


400  X   30  =    12000 

400  X  4  =  1600 

50  X  200  =  10000 

50  X  30  =  1500 

50  X  4  =  200 

6  X  200  =  1 200 

6  X  30  =  1 80 

6  X   4  =  24 

456  X  234  =  106704 

3.  The  following  will  show  why  the  first  figure  Oi  the 
product  must  be  written  under  its  multiplier: 

(   456  X       4  =     1824 
456  X  234  =    j   456  X     30  =  1368/0 

(     466    X    200   =    912/00 

456  X  234  =106704 

4,  Various  ways  in  which  the  partial  products  may  be 
written  : 

(0  456    (2)  456    (3)  456    (4)  456 

234          234          234          234 

1824        912          912  24 

i368          1824        1368  18 

912          1368          1824         12 

20 


106704  106704  105404  15 

IO 

16 

12 

8 
106704 


Science  and  Art  of  Ed 


5.  Multiplication  is  a  short  method  of  finding  the  sum  of 
a  number  of  repetitions  of  the  same  number. 

ADDITION.  MULTIPLICATION. 

4567  4567 

4567  4 

4567 

4567  18268 


18268 

1 6.  Some  Points  in  Division. 

1.  In  multiplication,  the  number  to  be  repeated  and  that 
denoting  the  number  of  repetitions  are  given  to  find  the 
sum  ;  in  division,  the  sum  and  the  repeated  number  are 
given  to  find  the  number  of  repetitions  ;  or  the  sum  and  the 
number  denoting  the  repetitions  may  be  given  to  find  the 
repeated  number. 

2.  Division  may  be  regarded  as  a  short  method  of  per- 
forming a  number  of  subtractions  with  the  same  subtra- 
hend. 

SUBTRACTION.  DIVISION. 

2193  243)  2I93  (9 

243  (l)  2187 


195° 
243  (2) 

1707 
243  (3) 

1464 
243  (4) 

1221 
243  (5) 

978 


Suggestions  for  Teaching  Numbers. 


978 
243  (6) 


735 
243  (?) 

492 

243  (8) 

249 
243  (9) 


3.  In  multiplication  two  factors  are  given  to  find  their 
product ;  in  division  the  product  and  one  of  the  factors,  to 
find  the  other. 

17.  Important  Divisibilities  of  Numbers. 

1.  A  divisor  of  several  numbers  is  a  divisor  of  their  sum 
and  difference. 

2.  A  divisor  of  the  sum  of  two  numbers  and  one  of  the 
numbers  divides  the  other. 

3.  A  divisor  of  a  number  is  a  divisor  of  any  multiple 
of  it. 

4.  A  number  is   not   divisible  by  any  number  but  its 
factors. 

5.  Dividing  one  of  the  factors  of  a  number  divides  the 
number. 

6.  Multiplying  the  divisor  divides  the  quotient. 

7.  Dividing  the  divisor  multiplies  the  quotient. 

18.  Meanings  of  Division. 

Of  the  following  indicated  division,  8-5-4,  three  different 
cases  may  be  assumed  :  i.  How  many  4*5  are  in  8  ?  2. 
Four  is  what  part  of  8  ?  3.  What  is  i  of  8  ?  Although  the 
three  answers  are  expressed  by  the  figure  2,  no  two  of  them 
represent  the  same  thing. 


1 52  Science  and  Art  of  Education. 

19*  Long  Division. 

1.  There  is  no  real  difference  between  short  division  and 
so-called  long  division;  both  aim  at  the  same  end  and  attain 
it  by  the  same  method.     In  short  division  most  of  the  work 
is  done  mentally,  but  in  long  division  the  larger  divisor 
makes  it  necessary  to  write  it. 

2.  A  few   short-division   problems   solved   by  the  long- 
division  process  forms  one  of  the  best  introductions  to  long 
division. 

20.  Greatest  Common  Measures. 

1.  The  G.  C.  M.  of  several  numbers  is  the  largest  factor 
common  to  all  of  them.     It  may  consist  of  a  prime  number 
or  of  the  product  of  several  prime  numbers. 

2.  When  the  numbers  are  small,  either  of  the  following 
methods  may  be  employed  to  find  the  G.  C.  M  : 

32 V     45     8,  ^3X3X3 


3  3  9     i5     27  45  =  3  X  3  X  5 


5 9  81  =3X3X3X3 


3  X  3  =  9,  G.  C.  M.  3  X  3  =  9,  G.  C.  M. 

3.  When  the  numbers  are  large  the  method  by  division 
must  be  employed.     Example  : 

1679)7981(4 
6716 

1265)  1679  (i 
1265 

414)1265(3 
1242 
""23)414(18 

£i 

184 
184 

By  the  following  reasoning  the  method  by  division  may 
be  proved.     In  the  example  given,  since  the  smaller  of  the 


Suggestions  for  Teaching  Numbers.  153 

two  numbers  is  not  an  exact  divisor  of  the  larger,  it  is 
not  their  G.  C.  M.;  but  since  (17,  i)  the  number  sought 
cannot  be  greater 'than  (1256)  the  difference  of  the  two 
numbers,  it  may  be  this  difference  ;  a  trial,  however,  shows 
that  it  is  not,  that  it  is  not  an  exact  divisor  of  (1679)  tne 
smaller  of  the  two  numbers.  Continuing  the  same  reason- 
ing, we  find  that  the  G.  C.  M.  cannot  be  greater  than  (414) 
the  difference  between  1265  and  1679,  and  as  a  trial  shows 
that  it  is  not  this  difference,  it  maybe  the  difference  between 
a  multiple  of  this  difference  and  1265,  and  this  is  found  to 
be  correct. 

21.  The  Least  Common  Multiple.         , 

1.  The  L.  C.  M.  of  several  numbers  is  the  smallest  num- 
ber that  contains  each  of  them  as  a  factor. 

2.  The  following  are  the   two   methods  of  finding  the 
L.  C.  M.;  that  by  factoring  being  the  more  easily  explained. 

10=  2  X  5 
18  =  2  X  3  X  3 
56  =  2X2X2X7 
75  =  3X5X5 


2X2X2X3X3X5X5X7  =  12600. 
18     56     75 


28     75 


i       9     28     15 


28 


2X5X3X3X28X5  =  12600. 

22.  Fractions. 

Though  fractions  have  received  considerable  attention  in 
the  preceding  pages,  a  few  more  thoughts  concerning  them 
remain  to  be  given. 

i.  A  so-called  compound  fraction  is  an  indicated  multL 
plication  of  fractions  and  not  a  fraction. 


ie|4  Science  and  -A  rt  of  Education. 

2.  What  is  called  a  complex  fraction  is  usually  an  indi- 
cated division  of  a  fraction  by  a  fraction. 

3.  Multiplying  a  fraction  by  a  fraction  is  taking  such  a 
part  of  the  multiplicand  as  the  divisor  is  of  the  unit. 

4.  Dividing  by  a  fraction  is  taking  the  dividend  as  many 
times  as  the  divisor  is  contained  in  the  unit. 

REMARK.  —  From  3  and  4  of  the  foregoing,  we  note  that, 
generally  speaking,  multiplying  by  a  fraction  divides,  and 
dividing  multiplies. 

5.  A  fraction  may  be  reduced  to  its  lowest  terms  by  fac- 
toring both  of  its  terms  and  cancelling  the  common  factors  ; 
or,  when  both  terms  are  large,  by  dividing  them  by  their 
G.  C.  D. 

6.  The  following  exercises  may  be  used  to  show  that  the 
value  of  a  fraction  is  not  changed  by  multiplying  or  divid- 
ing both  of  its  terms  by  the  same  number. 

*  =  *  =  *=*=*,  etc.;  J  =   f  =  A  =  A  =  A,  etc.; 


.;  J  =   f  =  A  =  A  =  A, 

.;  t  =  A  =  A=A  =  A, 


REMARK.  —  Exercises  like  the  foregoing  may  also  be  used  to 
show  that  fractions  of  unlike  denominators  may  be  reduced  to 
the  same  denominator  and  added  or  subtracted. 

7.  Reducing  several  fractions  of  different  denominators 
to  the  same  denominator,  by  multiplying  each  numerator  by 
all  the  denominators  except  its  own,  and  all  the  denomina- 
tors together  for  a  new  denominator,  multiplies  both  terms 
of  each  fraction  by  the  same  number. 

Illustrative  example  : 

9  .  4.  6^2X5X7^4X3X7^6X3X5^70    1    84   -   90 
357     3X5X7     5X3X7     7X3X5     105     105     105* 

Instead  of  finding  the  numerators  by  the  preceding 
method,  they  may  be  found  by  dividing  the  common 


Suggestions  for  Teaching  Numbers.  155 

denominator  by  the  denominator  of  each  fraction  and  mul- 
tiplying the  quotient  by  the  numerator.    • 

8.  The  numerator  of  a  fraction  may  be  divided  by  an  in- 
teger (whole  number)  by  first  multiplying  both  terms  of  the 
fraction  by  the  integer. 

Multiplying  the  denominator  of  a  fraction  by  an  integer 
divides  the  fraction  by  the  integer,  because  it  increases  the 
ratio  of  the  numerator  to  the  denominator  by  the  multiplier. 

9.  No  reason  can  be  assigned  for  the  inversion  of  the 
divisor  in  the  division  of  a  fraction  by  a  fraction,  but  its 
correctness  can  be  shown  by  means  of  an  analytic  explana- 
tion or  demonstration.     For  example,  let  it  be  required  to 
divide  \  by  |.     Explanation  :  One  third  is  contained  in  i 
three  times,  and  f  (being  twice  as  large)  one  half  as  often  ; 
that  is,  the  number  of  times  J  are  contained  in  i  ;  but  in  \ 
they  are  contained  one  eighth  as  often,  and  in  \  seven  times 
as  often  as  in  \.     Statement  of  analysis:     fXiXjX^= 
f  X  £.     In  this  statement  we  see  that  the  divisor  has  been 
inverted  ;  and  since  the  same  will  invariably  be  the  case,  we 
must  infer  that  inverting  the  divisor  and  then  multiplying 
give  the  correct  result. 

10.  The  correctness  of  the  foregoing  may  also  be  shown 
by  means  of  a  diagram. 

23.  Decimals. 

1.  Decimals  are  parts  of  things,  or  units,  in  which  the 
division  is  made  according  to  the  scale  of  tenths.     Decimal 
expressions,  though  not  decimals,  will  here  for  convenience 
be  treated  as  decimals. 

2.  Decimals,  being  derived  from  integers,  should  be  de- 
veloped from  them.     This  may  be  done  by  continuing  the 
division  as  far  below  the  decimal  point  as  may  be  thought 
necessary.     The  following  example  will  indicate  some  of  the 
steps  that  may  be  taken  to  introduce  the  subject : 


1 5  6  Science  and  Art  of  Education. 


1000,  100,  10,  I,  —  ,  ,  .   IOOO+ 100+  10+  I H 1 1 . 

10,  100  1000  '  10  '  loo  '  1000 

III  I     IOO      I       IO 

—  =.i;  =  .oi; =  .ooi.  —  = ;  = . 

10       IOO         1000  10    1000    IOO     1000 

IOO     IO   ,    I      III 

.  I +  .01 +  .001  =.III. = . 

1000    IOO  '  1000    1000 

I.I.    I      IOO  ,IO,    I     III 

—  H = = =  . i +  .01. +  .ooi=.  in. 

10  '  IOO    1000    1000   IOOO  '  1000   IOOO 

3.  The  pupils  should  be  led  to  see  or  to  discover  (i)  that 
the  point  is  the  distinguishing  mark  of  decimals,  and  that  it 
is  placed  before  them  to  separate  them  and  to  distinguish 
them  from  integers  ;  (2)  that  as  the  value  of  integers  de- 
creases from  left  to  right  and  increases  from  right  to  left,  so 
also  does  that  of  decimals  ;  (3)  that  the  value  of  a  decimal 
depends  upon  its  distance  from  the  point  ;  and  (4)  that  for 
every  place  a  decimal  is  moved  to  the  left  it  is  multiplied  by 
10,  and  for  every  place  it  is  moved  to  the  right  is  is  divided 
by  10. 

4.  Practice  should  be  given  in  writing  and  reading  deci- 
mals until  the  pupils  can  readily  do  either.    Decimals  should 
be  read  as  if  they  were  common  fractions,  the  name  of 
the  last  place  to  the  right  given  as  the  denominator.     Ex- 
ample :  In  0.00456,  the  last  place  to  the  right  is  that  of 
hundred-thousandths,  the  fraction  is  therefore  456  hundred- 
thousandths. 

REMARK. — Decimals  may  be  written  in  four  different  ways : 
i.  In  words  (three  hundredths) ;  2.  In  the  common  fractional 
form  (T£s) ;  3.  With  the  per- cent  sign  (3^) ;  4.  In  the  usual  form 
(-03). 

5.  Place  of  Point  in  Multiplication. — The  following  will 
show  how  the  rule  for  the  location  of  the  point  may  be  de- 
rived.    Taking  .5  X  .4  as  an  example,  if  we   discard  the 
points  and  multiply  5  by  4,  we  obtain  20  as  the  product ; 
but  the  multiplicand  is  not  5,  but  ^  of  it,  hence  the  prod- 
uct is  -jV  of  20,  or  2.0  ;  and  for  a  similar  reason,  since  the 


Suggestions  for  Teaching  Numbers.  157 

divisor  is  not  4,  but  fa  of  it,  the  last  found  product  is  not 
2.0,  but  -fa  of  it,  or  .20.  An  examination  of  the  number  of 
places  in  the  product  shows  that  it  is  equal  to  the  sum  of 
those  in  the  factors.  In  the  same  manner  may  the  rule  be 
derived  when  the  factors  contain  two  or  more  decimals. 

6.  Place  of  Point  in  Division. — If  in  .45  -f-  .5  =  .9,  we  dis- 
card the  points  and  perform  the  division,  we  obtain  9  as  the 
quotient  ;  but  since  the  dividend  is  not  45,  but  TJ-^-  of  it, 
the  quotient  must  be  T^  of  9,  or  .09.  This  is  the  quotient 
obtained  by  dividing  by  5,  ten  times  the  divisor,  and  is 
therefore  -fa  of  the  correct  quotient,  or  .9.  Here  we  observe 
that  the  number  of  decimal  places  in  the  quotient  is  that  by 
which  those  in  the  dividend  exceed  those  in  the  divisor. 
The  same  kind  of  reasoning  will  discover  the  rule  when 
both  terms  contain  several  decimals. 

24.  Analysis. 

I.  PROPORTION. — The  problems  usually  found  under  the 
head  of  proportion  in  books  on  arithmetic  can,  with  more 
benefit  to  the  pupils,  be  solved  by  analysis  and  cancellation. 
Simple  problems,  such  as  are  found  on  page  128,  should  at 
first  be  given,  and  their  length  and  difficulty  increased  as 
the  pupils  show  themselves  able  to  master  them. 

Problem  i. — If  in  9  days,  of  8  hours  each,  20  men  can 
build  a  wall  40  feet  long,  2  feet  thick,  and  6  feet  high,  how 
many  men  would  be  required  to  build  a  similar  wall  60  feet 
long,  3  feet  thick,  and  5  feet  high,  in  15  days,  of  12  hours 
each? 

REMARK. — Before  the  analysis  of  a  problem  is  commenced,  a 
statement  of  the  conditions  of  the  problem  should  be  made.  It 
should  also  be  observed  that  the  first  term  of  the  analysis 
should  be  of  the  same  kind  as  the  one  required. 

Statement  of  Conditions  : 

M.           d.  hrs.  ft.  I.  ft.  th.  ft.  h. 

20           9  8  40  2  6 

?         15  I?  6p  3  5 


158  Science  and  Art  of  Education. 


Statement  of  Analysis  : 


Analysis,  or  Explanation.  —  Since  the  work  can  be  done  in 
9  days  by  20  men,  it  would  require  9  times  as  many  men 
to  it  in  i  day,  and  3^  as  many  in  15  days  as  in  i  day. 
That  is,  if  they  work  8  hours  a  day  ;  but  i  hour  a  day  would 
require  8  times  as  many  men  as  8  hours,  and  12  hours  a  day 
-fx  as  many  as  i  hour.  That  is,  if  they  make  it  40  feet 
long;  but  i  foot  long  would  require  -fa  as  many  men 
as  40  feet,  and  60  feet  60  times  as  many  as  i  foot.  That  is, 
provided  they  make  it  2  feet  thick  ;  but  i  foot  thick  would 
require  one  half  as  many  as  2  feet,  and  3  feet  three  times  as 
many  as  i  foot.  That  is,  if  they  make  it  6  feet  high  ;  but  i 
foot  high  would  require  one  sixth  as  many  men  as  6  feet* 
and  5  feet  five  times  as  many  as  i  foot,  t 

Of  every  problem  twice  as  many  problems  can  be  made 
as  it  has  terms.  Of  the  following  eleven,  made  from  the 
foregoing,  only  the  statements  of  the  conditions  and  of  the 
analyses  will  be  given.  The  problems  can  be  read  from  the 
statements. 

Problem  2. 


Problem  3. 

?x!°x_'_ 

I          I  15 

Problem  4. 


M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

15 

15 

12 

60 

3 

5 

? 

9 

8 

40 

2 

6 

7  : 

<IX1>: 

*i°: 

*~3X 

I         5' 

<  -  = 

M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

20 

9 

8 

40 

2 

6 

15 

? 

12 

60 

3 

5 

I 

12        40  ' 

*$?: 

2 

IX6) 

i 

M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

15 

15 

12 

60 

3 

5 

20 

? 

8 

40 

2 

6 

12, 

I     I 

40. 

I 

2        I  N 

<6  = 

F' 

8    60 

I 

3 

I        5" 

I 

Suggestions  for  Teaching  Numbers.  159 


M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

Problem  5. 

20 

9 

8 

40 

2 

6 

15 

15 

\ 

60 

3 

5 

-x-x-  ) 

<9X 

£x 

-X- 

xx-x 

-x,- 

xf  = 

12. 

I        i        15  ' 

1 

15 

40      I 

2 

i      6 

M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

Problem  6. 

15 

15 

12 

60 

3 

5 

2O 

9 

? 

40 

2 

6 

L2  x  l±  x  -  : 

<i_5) 

<-X 

-X^-° 

x-zx 

2         I 

X-  = 

8. 

i      i     20' 

i 

9 

OO          I 

3 

I         5 

i 

M. 

d. 

hrs. 

ft.  1. 

ft.  th. 

ft.  h. 

Problem  7. 

20 

9 

8 

40 

2 

6 

15 

15 

12 

•> 

3 

5 

4-  X  -  X  -5 

x-> 

<^> 

<5X'-2 

X-X 

i      6 

x-- 

60. 

I          20         I 

9 

8       i 

I 

3      I 

5 

M. 

d. 

hrs. 

ft.  1, 

ft.  th 

.    ft.  h. 

Problem  8. 

15 

15 

12 

60 

3 

5 

20 

9 

8 

? 

2 

6 

Q  x  -  X  -° 

I 

Xr5 

I 

:?2xr 

x^x 

i*f 

*-;= 

40. 

M. 

4 

hrs. 

ft.  1. 

ft.  th 

.    ft.  h. 

Problem  9. 

20 

9 

8 

40 

2 

6 

15 

15 

12 

60 

? 

5 

?X-LX!1X 

-X- 

_5_X- 

12 

4£x_ 

I       6 

X-  = 

3, 

I        20         I 

9 

1 

i       6 

K>        I 

5 

M. 

d 

hrs. 

ft.  1 

ft.  th, 

,    ft.  h. 

Problem  10. 

15 

15 

12 

60 

3 

5 

20 

9 

8 

40 

? 

6 

3X±X-X 

£   x 

?x_ 

ix?x 

5?x- 

i       5 

I  __ 

2. 

i       15        I 

15 

I      i 

2        I 

I        A 

^0        I 

6 

M. 

'  d. 

hrs. 

ft.  1. 

ft.  th 

.    ft.  h 

Problem  II. 

20 

9 

8 

40 

2 

6 

15 

15 

12 

60 

3 

? 

160  Science  and  Art  of  Education. 


M. 

d. 

hrs. 

ft.  l. 

ft.  th. 

ft.  h. 

Problem  12. 

15 

15 

12 

6c 

3 

5 

2O 

9 

8 

40 

2 

p 

I      "  15  '  *    I    "  15         I  '  "  12  '  "  I  "    I    "  40  "  I  "  2 

REMARK. — Until  the  pupils  can  themselves  see  the  reason  for 
doing  so,  they  may  be  told  that  the  reasoning  must  begin  and 
the  units  be  taken  in  the  horizontal  line  of  the  statement  of  the 
conditions  in  which  all  the  numbers  are  given.  As  will  be 
seen,  the  reasoning  in  all  the  foregoing  begins  in  the  upper 
line. 

The  following  problems  can  all  be  solved  by  the  foregoing 
method,  and  in  most  cases  with  much  less  work  than  the  usual 
method  requires  : 

i.  If  it  takes  13,500  bricks,  8  inches  long,  4  inches  wide, 
and  2  inches  thick,  to  build  a  wall  200  feet  long,  20  feet 
high,  and  16  inches  (i£  feet)  thick,  how  many  bricks,  10 
inches  long,  5  inches  wide,  and  2^  inches  thick,  would  be 
required  to  build  a  wall  600  feet  long,  24  feet  high,  and  20 
feet  thick  ? 

Brick.  Wall. 

Bricks.         in.  1.      in.  w.      in.  th.        ft.  1.          ft.  h.  in.  th. 

13500         842         200         20         16  =  f  ft. 

?  10  5  2^          600  24  20  ft. 


373,248. 

2.  If  6  men  in  4  months,  working  26  days  for  a  month 
and  12  hours  a  day,  can  set  the  type  for  24  books  of  300 
pages  each,  60  lines  to  the  page,  12  words  to  the  line,  and 
an  average  of  6  letters  to  the  word,  in  how  many  months  of 
24  days  each,  and  10  hours  a  day,  can  8  men  and  4  boys 
set  the  type  for  10  books  of  240  pages  each,  52  lines  to  the 
page,  1 6  words  to  the  line,  and  8  letters  to  the  word,  2  boys 
doing  as  much  as  a  man  ? 

M.     mo.      d.       hrs.  books,  pages,   lines,    words,  letters. 

(8  men -{-4  boys   6  4  26  12  24  300  60   12   6 
=  10  men.)   10   ?  24  10  10  240  52   16   8 


Suggestions  for  Teaching  Numbers.  1 6 1 


3.  How  many  cords  of  wood  in  a  pile  80  feet  long,  12 
feet  high,  and  4  feet  thick  ? 

Cords.  ft.  1.  ft.  h.  ft.  th. 

i  8  4  4 

?  80  12  4 

J  x  f  x  Y  x*  x  V  x  *  x  f  =  gj 

4.  How  many  cubic  yards  of  earth  is  taken  from  a  ditch 
120  feet  long,  4  feet  wide,  and  9  feet  deep? 

Cu.  yd.  ft.  1.  ft.  w.          ft.  d. 

1333 

120  4  9 

|XiXHAXJ-fiX4X^XiXf=  160. 

5.  How  many  perches  of  stone  in  a  wall  36  feet  long,  2$ 
feet  thick,  and  5  feet  high  ? 

Perches.  ft.  I.  ft.  th.  ft.  h. 

i  i6J  ij  i 

?  36"  2*  5 

tX^X}X\«-XiXfXiXfXf=  18.18  -f . 

6.  What  is  the  number  of  bushels  of  wheat  a  bin  9  feet 
long,  5^  feet  wide,  and  if  feet  deep. 

Bu.  ft.  1.  ft.  w.  ft.  d. 

(i£  cu.  ft.  =  i  i  ij  i  i 

bu.,  nearly.)  ?  9  5^3$ 

|X-iXtXfXjXYXiXY  =  144- 

7.  Required  the  number  of  gallons  of  water  in  a  tank  12 
feet  long,  3^  feet  wide,  and  if  feet  deep. 

Gal.  ft.  1.  ft.  w.          ft.  d. 

(i  cu.  foot  =  i\  gal-  7^  i  i  i 

Ions,  nearly.)  ?  12  3^  if 

¥-xYxi><Yxi  x  Y-  x  ix  \  =  500, 


1  62  Science  and  Art  of  Education. 

II.  SIMPLE  INTEREST.  —  Interest  can  more  readily  and 
intelligently  be  taught  to  beginners  by  stating  the  number 
of  cents  on  the  dollar  than  by  using  the  term  per  cent. 
Six  cents  on  the  dollar,  for  example,  is  6  per  cent. 

If  the  time  is  given  in  years  and  months,  it  may  be  re- 
duced to  the  fraction  of  a  year  or  to  months  ;  and  if  it  is 
given  in  years,  months,  and  days,  it  is  more  conveniently  re- 
duced to  days,  counting  30  days  to  the  month  and  12 
months  to  the  year.  If  exact  interest  is  required,  365  days 
must  be  taken  for  a  year,  and  the  correct  number  of  days 
between  the  dates  found. 

Problem  i  :  What  is  the  interest  of  $804  dollars,  at  6c 
on  the  dollar,  for  9  years  10  months  and  5  days  ? 


p. 

int.                               time. 

$1 
$804 

6c                         i  yr. 
?             9  yr.  10  mo.  5  d. 

f  X*| 

L±  X 

rirr  X  ^*-5-  =  $475-°3- 

p. 

int.                             time. 

Problem  2  : 

$i 
$804 

?                       i  yr. 
1-      475°3C        9  yr-  10  mo.  5d. 

47503 

X* 

1  ._       V   .3.60    y        1        —   £.r 

nrs"  ^    T    ^  "5oT  —  t"" 

p. 

int.                          time. 

Problem  3  : 

$i 

6c                    i  yr. 

JJJL  X  i  X  AlfW.  X  -gfa  =  3545  days  =  9  yr.  10  mo.  Sd. 

P.  int.  time. 

Problem  4  :  $i  6c  ? 

9  vr-  IQ  rnQ.  $d. 


x  f  x  M*  = 


Suggestions  for  Teaching  Numbers. 


Problem  5  : 

P.                          int. 

$i                  6c 
?               47503£ 

time. 

i  yr. 
9  yr.  10  mo.  5  d. 

ix* 

x  AlfJU.  X  ^°  X  ^ 

r6  =  $804. 

Problem  6  : 

P.                       int. 

?                 6c 
$804        475°3C 

time. 

i  yr. 
9  yr.  10  mo.  5d. 

The  following  problem  contains  dollars  and  cents  in  the 
principal  and  a  fraction  in  the  rate  : 

P.  int.  time. 

Problem  7  :         $1.00  5^c  i  yr. 

$345.75  2  yr.  4  mo.  gd. 

3-842 

V  X  Tfc  X  -^f11  X  ,**  X  ifi  =  $43.49- 

3 

Explanation. — The  interest  of  100  cents,  or  $i,  is  ^ 
cents,  of  i  cent  it  is  TJ7  as  much,  and  of  34575  cents  it  is 
34575  times  as  much  as  of  i  cent.  That  is  for  360  days,  or 
i  year  ;  for  i  day  it  is  ^fa  as  much,  and  for  849  days  (2  yr. 
4  mo.  9  d.)  819  times  as  much  as  for  i  day. 

The  cancellation  can  be  considerably  simplified  by  di- 
viding both  numerator  and  denominator  by  1000  ;  that  is, 
by  striking  out  3  noughts  of  the  denominator  and  pointing 
off  three  places  in  the  principal  of  the  numerator. 

By  continuing  the  division  of  the  numerator  by  the  de- 
nominator or  its  factors  to  as  many  decimals  as  may  be  nec- 
essary for  accuracy,  the  whole  denominator  can  generally 
be  cancelled. 

III.  PERCENTAGE. — The  following,  is  one  of  the  simplest 
methods  of  introducing  percentage,  the  pupils  having 
learned  the  numbers  at  least  as  far  as  joo.  The  teach ef 


164  Science  and  Art  of  Education. 

should  say  that  the  terms  here  presented  are  only  other 
names  for  the  fractions  with  which  they  are  already  famil- 
iar. Instead  of  writing  the  words  per  cent.,  the  sign  ($) 
meaning  hundredths  should  be  used. 

100$  —  {%%  ~  i,  the  whole  of  anything  ;  75$  =  -^  =  f  ; 

5o$  =  A°o  =  i;  25*  =  *-  =  *;  2o^  =  TVo  =  i;  «>*  = 
iW=  A ;  s£  =  -db-  =  A ;  i*  =  T£O  ;  9°$  =  A ;  M  = 
i;  7<>*  =  A;  6<#  =  f ;  4o#  =  i;  33i#  =  -i;  i6f*  =  i; 

12^  =  |;  and  (510  =  A« 

Many  oral  problems  should  be  given  to  familiarize  the 
pupils  with  the  new  terms  and  with  the  applications  of  per- 
centage. 

The  analytic  method  of  solution  applies  as  well  to  per- 
centage as  to  proportion  and  other  similar  subjects. 

NOTE. — Every  number  is  100  per  cent  (or  the  whole)  of 
itself. 

Problem  i  :  4  is  what  %  of  5  ? 

No.  % 

(No.  =  number.)  5         100         ^  X  -J-  X  f  -  80. 

4  ? 

Explanation. — Since  5  is  100$,  i  is  \  as  many$,  and  4,  4 
times  as  many  as  i. 

Problem  2  :  4  is  80$  of  what  number  ? 

No.  * 

?         ioo        \  X  *V  X  H-  =  5- 

4  80 

Explanation. — Since  4  is  80$  of  the  number,  i$  of  it  is 
-fa  of  4,  and  100$,  or  the  whole  of  it,  ioo  times  as  many. 
Problem  3  :  What  is  80$  of  5  ? 

No.  % 

5  ioo  \  X  Th-  X  -8T°-  =  4- 
?           80 

Problem  4  :  If  4  is  80$  of  some  number,  what$  of  it  is  5  ? 


Suggestions  for  '1'eachtng  Numbers.  165 

No.  % 

5  ?         V  X  i  X  f  =  ioo. 

4         80 

Problem  5  :  By  selling  my  cow  for  $40  I  gained  25$  on 
its  cost  ;  what  did  it  cost  me  ? 

REMARK.  —  Adding  25^  (the  gain)  to  ioo#  (the  cost)  and 
we  have  125  %  of  the  cost. 

No.  % 

40        125         Y-X  ilr  X^  =  32. 

?  IOO 

Problem  6  :  On  counting  my  money  I  found  that  $24  was 
2o#  less  than  I  had  when  I  left  home  ;  how  much  had  I 
spent  ? 

REMARK.  —  Subtracting  20%  from  ioo#,  and  we  have  8o#  ; 
what  was  left. 

No.  % 

24      80      VxA-xv=-6. 


REMARK.  —  The  pupils  should,  as  soon  as  possible,  be  led  to 
solve  percentage  problems  by  the  fractional  method. 

IV.  TRUE  DISCOUNT.  —  In  true  discount  the  present  worth 
corresponds  to  the  principal  in  simple  interest,  the  dis- 
count to  the  interest,  and  the  debt,  or  sum  discounted,  to 
the  amount.  When  the  sum  to  be  discounted,  the  rate,  and 
the  time  are  given,  to  find  the  present  worth,  the  problem  is 
the  same  as  having  given  the  amount,  rate,  and  time,  to  find 
the  principal. 

Problem  :  I  owe  $540,  due  in  4  years  without  interest, 
money  being  worth  $5$  ;  what  sum  would  discharge  the 
debt  to-day  ? 

Explanation.  —  As  $540  is  the  amount  of  the  present 
worth  of  the  debt  due  in  4  years  at  5$,  we  must  find  the 
amount  of  $i  for  4  years  at  5  #.  The  interest  of  $i  at  5$ 
for  4  years  is  20  cents,  and  this  added  to  the  dollar  makes 

'^Mfi^V 

NIVERSI1 

\w  CU;  jFoaN'> 


1 66  Science  and  Art  of  Education. 

$1.20,  the  amount.  Now,  considering  it  as  a  case  in  simple 
interest,  and  we  have  given  two  amounts  and  the  principal 
of  one,  to  find  that  of  the  other.  As  will  be  observed, 
therefore,  two  operations  are  required  ;  the  first,  to  find  the 
amount  of  $i  ;  the  second,  to  find  the  present  worth.  The 
following  are  the  statements  for  the  second  part  of  the  so- 
lution : 

P.  amt. 

(P.  =  present  $1.00     $1.20 

worth.)  ?  540 

^  X  Tib  X  -^f2-*  =  45°  —  required  present  worth. 
V.  BANK   DISCOUNT. — Bank   discount  differs  from  true 
discount  in  two  respects  :   i.  In  being  the  interest  on  the 
face  of  the  note  ;  2.  In  adding  3  or  4  days  of  grace  to  the 
required  time. 

REMARK.— The  face  less  the  discount  equals  the  proceeds. 

Explanation. — Since  the  proceeds  are  found  by  subtract- 
ing the  interest  (discount)  from  the  face  of  the  note,  hence, 
when  the  proceeds  are  given  and  the  face  value  is  required, 
the  proceeds  of  $i  must  be  found;  then  the  proceeds  of  the 
dollar  bear  the  same  relation  to  the  dollar  as  the  given  pro- 
ceeds do  to  the  required  face  of  the  note.  Here,  also,  it 
will  be  observed,  two  operations  are  required :  the  first,  to 
find  the  proceeds  of  one  dollar  ;  the  second,  to  find  the  re- 
quired face  of  the  note. 

P.  int.         time. 

i.     $1.00     6c.     36od.     f  X-j-5irX-9T3-  —  .0155, discount  on  $i. 
$1.00      ?        93d.      i.oo— .0155— .9845,  proceeds  of  $i. 

Proceeds.  Face. 

$0.9845  $' 

$600  ? 

(0        t  X  TgW  X  ^  —  609,446  +       required  face. 
(2) .      i  X  ^  X  UULJAO.  =  609,446  +      " 
REMARK.— Number  (2)  is,  perhaps,  the  simpler  operation. 


Suggestions  for  Teaching  Numbers.  167 

VI.  TIME  PROBLEMS. — Time  relations  are  best  repre- 
sented by  the  divisions  of  horizontal  lines. 

Problem  i  :  What  time  of  day  is  it  when  the  time  to  mid^ 
night  is  twice  the  time  past  noon  ? 

Solution. —  N.      p.      t    .MfIM.    The   time   past  noon  and 

the  time  to  midnight  equal  3  times  the  time  past  noon  ; 
hence,  the  time  from  noon  to  midnight,  or  12  hours,  is  3 
times  the  time  past  noon,  and  once  the  time  past  noon,  or 
the  required  time,  is  4  o'clock  p.  M. 

Problem  2  :  What  time  of  day  is  it  when  the  time  past 
noon  is  £  of  the  time  to  midnight  ? 

Solution. —     ty-^  F-^  i  K^-N-     The  time  to  midnight  and 

half  the  time  to  midnight,  or  f  the  time  to  midnight,  equal 
the  time  from  noon  to  midnight,  or  12  hours  ;  hence,  %  the 
time  to  midnight  equals  $  of  12  hours,  or  4  hours,  and  f  of 
the  time  to  midnight  equal  8  hours,  and  the  time  is  4 
o'clock  P.M.,  the  same  as  that  of  the  previous  problem. 

Problem  3  :  Required  the  time  of  day  when  the  time 
past  noon  equals  J  of  the  time  past  midnight. 

Solution.—  M-M'M  .  M  .  K^-K  P-  Since  the  time  past 
noon  is  J  of  the  time  past  midnight,  the  time  before  noon, 
or  from  midnight  to  noon,  must  be  f  of  the  time  past  mid- 
night, and  this  is  12  hours.  If  £  of  the  time  past  midnight 
is  12  hours,  \  of  it,  the  time  past  noon,  is  J  of  12  hours,  or 
4  hours,  and  the  required  time  is  4  o'clock  P.M. 

Problem  4  :  What  is  the  hour  of  day  when  the  time  to 
noon  is  ^  of  the  time  to  2  o'clock  P.M  ? 

Solution.—    5-HN-H  ,  K  i  **  i  K2  p-^      If   the  time   to 

noon  is  £  of  the  time  to  2  o'clock  P.M.,  then  the  time  past 
noon,  or  2  hours,  must  be  f  of  the  time  ;  and  if  £  of  the 
time  equal  two  hours,  £  of  it,  or  the  time  to  noon,  is  i  of  2 
hours,  or  £  an  hour,  and  the  time  required  is  n  o'clock  A.M. 


1 68  Science  and  Art  of  Education. 

VII.  AGE  PROBLEMS. — Age  relations  are  best  repre- 
sented by  the  divisions  of  vertical  lines. 

REMARK. — The  difference  in  the  ages  of  two  persons  re- 
mains the  same  as  long  as  both  of  them  live.  This  fact  serves 
as  key  to  the  solution  of  age  problems. 

Problem  i  :  John  is  now  4  years  of  age  and  Frank  is  10  ; 
in  how  many  years  will  John  be  f  as  old  as  Frank  ? 

Solution. — The  difference  of  their  ages  is  6  years,    ^Frank 
and  this,  as  the  lines  show,  will  be  £  of  Frank's 
age  at  the  required  time.     As  John's  age  will  then   ~^ 
be  f   of  Frank's,  it  will   be   twice  6  years,  or  12 
years,  and  since  he  is  now  4,  the  required  time  is 
the  difference  between  12  and  4,  or  8  years. 

Problem  2  :  Sarah  is  1 1  years  of  age  and  Alice  is  20 ; 
how  long  since  Sarah  was  i  as  old  as  Alice  ? 

^.  A  lice 

Solution. — The  difference  oftheir  ages,  9  years, 
was  \  of  the  age  of  Alice  at  the  required  time  ; 
hence  Alice  was  18  years  of  age  when  Sarah  was 
\  as  old  ;  and  this  was  two  years  ago. 

Problem  3  :  Twelve  years  ago  I  was  \  as  old  as  Mr. 
Jones,  now  I  am  f  as  old  ;  what  is  my  present  age  ? 

Solution. — Looking  at  the  divisions  of  the  Jones 

lines,  and  we  find  that  12  years  ago  the  dif-      T12  yea  s   ^ 
ference  of  their  ages  was  -J  of  Jones'  age,    ^    »  "  M  «i  • 
and  now  is  $  of  it  ;  but  as  the  difference      -  -  %  -  56    H» 
does  not  change,  evidently  \  of  Jones'  age    %        j        ^ 
12  years  ago  was  ^  of  what  it  now  is,  and  f       _L 
of  it  then  f  of  what  it  now  is.     From  this  we  see  that  12 
years  ago  Jones  was  f  as  old  as  he  now  is,  and  since  he  now 
is  f,  12  years  must  be  the  i  which  he  has  in  these  years 
added.     If  12  years  equal  £  of  Jones'  present  age,  he  is 
now  36,  and  I  am  f  x>f  36,  or  24. 


Suggestions  for  Teaching  Numbers.  169 

Problem  4  :  Sarah  is  now  3  times  as  old  as  Martha,  but  in 
9  years  will  be  twice  as  old  ;  how  old  is  each  now  ? 

Solution. — From  the  divisions  of  the  lines  Sarah 

..-  ,     .  T  9  years  -r 

we  see  that   the  difference  of    their  ages  is 

now  twice  Martha's  age  and  in  9  years  will  be 

once  her  age  ;  but  as  the  differences  are  the 

same,  twice  Martha's  age  now  is  once  what 

it  will  be  in  9  years,  and  once  her  age  now  is 

£  of  what  it  will  then  be.     Since  Martha's  age 

will  then  be  f  of  what  it  now  is,  she  must  in 

9  years  add  the  other  |  ;  and  if  9  years  equal  -j-  of  her  age 

then,  it  must  be  her  present  age,  and  Sarah's  is  3  times  9, 

or  27  years. 

REMARK. — If  in  the  foregoing  problem  the  question  were, 
how  old  will  each  be  then,  the  following  would  be  the  solution, 
differing  only  in  one  point  from  the  preceding  : 

Solution. — From  the  divisions  of  the  lines  we  observe 
that  the  difference  of  their  ages  is  now  twice  Martha's  age, 
and  in  9  years  will  be  once  her  age  ;  but  as  the  differences 
are  the  same,  2  times  Martha's  age  now  is  once  what  it  will 
be  in  9  years,  and  once  her  age  now  is  £  of  what  it  will 
then  be.  Since  Martha's  age  will  then  be  £  of  what  it  now 
is,  she  must  in  9  years  add  the  other  £  ;  and  if  9  years 
equal  •£  of  her  age  then,  f,  or  the  whole  of  it,  will  be  18 
years,  and  Sarah's  will  be  2  times  18  years,  or  36  years. 

VIII.  WATCH  AND  CHAIN  PROBLEMS. — Problem  i  :  A 
man  had  2  watches  and  only  i  chain.  If  the  chain  be  put 
upon  the  first  watch  it  wfll  make  its  value  twice  that  of 
the  second  ;  and  if  it  be  put  upon  the  second  watch  it  will 
make  its  value  3  times  that  of  the  first  ;  if  the  value  of  the 
first  watch  is  $30,  what  is  that  of  the  second,  and  of  the 
chain  ? 

REMARK. — The  equations  are  designed  to  indicate  the  rela- 
tions of  the  parts  of  the  problem  and  thus  to  aid  the  solution. 


Science  and  Art  of  Education. 


Solution.  —  As  the  first  watch  f.  w.  &  ch.  =  2  s.  w.;  3  s.  w.  =  whole. 

and  chain  are  together  worth  •;  s-  w-  =  ^  of  w|>ole' 

&  s.  w.  &  ch.  =  3  f.  w.;  4  f.  w.  =  whole. 

twice  as  much  as  the  second,  .-.  f.  w.  =  y±  of  whole. 


if  to  this  we  add  the  second  M+U  =  *;H-  A  =  A- 

we  have  3  times  the  second  for  the  whole,  and  consequently 
the  second  is  J  of  the  whole.  In  the  second  condition  we 
have  the  second  watch  and  chain  worth  3  times  as  much  as 
the  first  ;  if  to  this  we  add  the  first,  we  have  4  times  the  first 
for  the  whole,  and  the  first  is  J  of  the  whole.  Since  the  first 
watch  is  worth  $30,  the  value  of  the  whole  is  $120,  that 
of  the  second  $40,  and  -fy,  that  of  the  chain,  $50. 

IX.  FISH  PROBLEMS.  —  Problem  :  The  head  of  a  fish 
weighs  10  Ibs.,  the  tail  weighs  as  much  as  the  head  and  -J 
the  body,  and  the  body  weighs  as  much  as  the  head  and 
the  tail  ;  what  is  the  weight  of  the  fish  ? 

Solution.  —  Make  a  sketch  of  the  fish,  divide  it  into  head, 
body,  and  tail,  and  upon  each  part  place  the  number  given 
to  it  in  the  problem. 


The  sketch  of  the  body  of  the  fish  shows  that  20  Ibs. 
and  i  the  body  is  the  whole  body,  but  whatever  added  to  a 
£  makes  the  whole  must  be  the  other  half ;  therefore  20  Ibs. 
must  be  the  other  -J-.  If  \  the  body  weighs  20  Ibs.,  the 
\whole  of  it  weighs  40  Ibs.,  and  the  fish  —  head  10,  body 
40,  tail  30  =  80  Ibs. 

.X.  HOUND-HARE  PROBLEMS. — Problem  i  :  A  hare  is  20 
leaps  before  a  hound  and  takes  4  leaps  to  the  hound's  3, 
but  3  of  the  hound's  leaps  are  equal  to  6  of  the  hare's  ;  how 
many  leaps  must  each  take  until  the  hare  is  caught? 

Solution  :  First  make  a  graphic  representation  or  illustra- 
tion of  the  conditions  of  the  problem. 


Suggestions  for  Teaching  Numbers.  1 7 1 

An  examination  of  the  accompanying  repre-     hound,   hare, 
sentation    of    the   conditions  of    the  problem         3         4 
shows  that  while  the  hound   takes  6  of    the         s    = 
hare's  leaps  the  hare  takes  but  4,  and  thus  loses  2.     If  the 
hare  loses  2  in  running  4,  to  lose  i  it  must  run  \  of  4,  or  2, 
and  to  lose  20  if  must  run  20  times  2,  or  40. 

When  the  hound  runs  3  it  gains  the  2  which  the  hare 
loses;  hence,  to  gain  i  it  must  run  £  of  3,  or  ij,  and  to  gain 
20  it  must  run  20  times  i£,  or  30. 

Problem  2  :  A  rabbit  is  60  leaps  before  a  hound  and 
takes  9  leaps  to  the  hound's  3,  but  2  of  the  hound's  equal  7 
of  the  rabbit's  ;  how  many  leaps  will  each  take  until  the 
rabbit  is  caught  ? 

Solution. — Make  a  graphic  representation  of  hound,  rabbit, 
the  conditions,  and  then,  as  the  numbers  of 

the  hound's  leaps  are  unlike,  multiply  each  of       — ~ 

the  conditions   by  such  a   number   as   shall        e     =    21 
make  them  alike,  or  the  same.     The  remainder  of  the  solu- 
tion is  the  same  as  in  the  previous  problem. 

XI.  ALLIGATION. — Problem  :  How  shall  I  combine  sugars 
that  cost  me  6c,  7C,  I3C,  and  i4c  a  Ib.  so  that  I  may  be  able 
to  sell  the  mixture  at  gc  a  Ib  ? 

NOTE. — The  only  conditions  to  be  observed  in  the  solution 
of  problems  of  this  kind  are  (i)  that  the  sum  of  the  gains  shall 
equal  that  of  the  losses,  and  (2)  that  every  ingredient  upon 
which  there  is  a  gain  shall  be  combined  with  one  upon  which 
there  is  a  loss. 

REMARK. — The  arrangement  of  the  solution  of  the  problem 
here  given  is  the  usual  one,  except  the  horizontal  line  that 
separates  the  losses  and  gains. 

Solution    i. — On    a    pound   of   6c  p  fcet  Diffi 

sugar  sold  for  gc  there  there  will  be  a 
gain  of  3C,  on  a  pound  of  7c  sugar  Average 
sold  for  gc  there  will  be  a  gain  of  2c,        9 
on  a  pound  of  I3C  sugar  sold  for  gc 
there  will  be  a  loss  of  4C,  and  on  a 


172  Science  and  Art  of  Education. 

pound  of  140  sugar  sold  for  90  there  will  be  a  loss  of  50. 
Now,  since  the  gains  and  losses  must  equal  each  other, 
if  we  take  5  pounds  of  that  on  which  there  is  a  gain  of 
3c  and  3  pounds  of  that  on  which  there  is  a  loss  of 
5c,  the  two  will  balance  each  other;'  and  if  we  take  2 
pounds  of  that  on  which  there  is  a  gain  of  2C  and  i  pound 
of  that  on  which  there  is  a  loss  of  4C,  they  will  balance 
each  other. 

Solution  2. — If  we  take  4  pounds  of  that  on  which  there 
is  a  gain  of  3C  and  3  pounds  of  that  on  which  there  is  a 
loss  of  4c,  they  will  balance  each  other  ;  and  if  we  take  5 
pounds  of  that  on  which  there  is  a  gain  of  2c  and  2 
pounds  of  that  on  which  there  is  a  loss  of  5c,  they  will  bal- 
ance each  other. 


GEOGRAPHY. 

Introductory  Considerations.  —  Geography  is  generally 
classed  among  the  dry  subjects,  but  the  dryness  is  not  so 
much  in  the  subject  as  it  is  in  the  teachers  and  the  teach- 
ing. A  real  teacher  can  invest  any  subject  with  interest, 
but  a  lesson-hearer  kills  even  the  interest  that  naturally  in- 
heres in  a  subject. 

Much  of  the  matter  that  has  in  the  past  been  taught  as 
regularly  belonging  to  geography,  and  not  a  little  of  that 
still  taught  to  children,  is  not  of  the  most  inviting  nature. 

No  greater  mistake  can  be  made  in  teaching  beginners 
than  requiring  them  to  shut  their  eyes  to  the  world  in 
which  they  live  and  to  look  into  a  book  where  all  is  strange 
and  meaningless  ;  yet  this  is  the  method  generally  pursued. 
The  children's  experiences,  which  should  be  used  as  start- 
ing-points, are  not  only  ignored,  but  regarded  as  of  no 
value. 

Definitions,  of  whose  meaning  the  children  can  have  no 
idea,  are  frequently  the  food  which  their  mental  stomachs 
are  given  to  digest.  After  they  are  supposed  to  have 
learned  these,  then,  with  their  undeveloped  imagination, 
they  are  expected,  from  the  study  of  a  globe,  to  form  a 
conception  of  the  earth  as  a  whole,  and  afterwards  to  di- 
vide it  into  its  so-called  members,  and  these  again  into  sub- 
members,  and  so  on,  until  the  smallest  division  has  been 
reached  ;  this  method  of  procedure  being  followed,  upon 
the  ground  that  in  everything  studied  or  conceived,  that  is 
composed  of  parts,  one  must  begin  with  analysis — with  the 

173 


174  Science  and  Art  of  Education. 

whole  and  go  to  its  parts  ;  but  such  a  strain  at  universality, 
the  law  "  from  the  whole  to  its  parts,"  will  not  bear  ;  and  a 
little  reflection  upon  the  manner  in  which  the  mind  builds 
its  spacial  forms  will  show  the  erroneousness  of  the 
method. 

The  suggestions  which  follow  are  a  departure  both  in 
matter  and  method  from  what  usually  passes  for  geography, 
but  are  in  harmony  with  the  best  in  that  line  of  instruc- 
tion. 

The  study  of  geography  should  be  commenced  in  the 
primary  school,  with  what  the  children  can  observe,  and 
should  be  largely  conversational.  Its  object  should  be  to 
awaken  an  interest  on  the  part  of  the  children  in  the 
boundless  forms  of  nature  that  meet  them  on  every  hand. 

The  work  of  the  primary  and  others  of  the  lower  grades 
of  schools  should  embrace  the  following  topics  : 

1.  Land. — i.  Its  forms  in  meadows,  uplands,  plains,  hills, 
and  mountains. 

2.  The  material  of  which  land  is  composed,  namely,  soils 
and  rocks. 

3.  The  materials  of  which  the  different  kinds  of  soils 
are  composed,  namely,  loam,  sand,  gravel,  and  clay. 

REMARK. — The  children  should  examine  the  different  kinds 
of  soil. 

4.  The  part  each  of  the  two  soils  (top  and  sub)  performs 
in  the  growth  of  vegetation. 

5.  The  kinds  of  soil  certain  crops  demand,  the  prepara- 
tion and  fertilization  of  the  ground  for  the  reception  of  the 
seeds,  the  time  and  mode   of   planting,  and  care   of  the 
plants. 

6.  The  changes  which  land-forms  are  undergoing,  and 
their  causes. 

7.  The  influence  of  land-forms  upon  climate. 

NOTE. — The  children  should  make  models  in  sand  of  the 
forms  of  tend  which  they  have  observed ;  this  will  enable  them 


Suggestions  for  Teaching  Numbers.  175 

later  on  in  their  study,  when  observing  a  model,  to  look  with 
their  imagination  beyond  it  to  that  which  it  represents. 

2.   Water. — i.   The    forms    of    water — ice,    liquid,   and 
vapor. 

2.  How  ice  and  vapor  are  formed  and  how  returned  to 
the  liquid  state. 

NOTE. — Whenever    necessary    and     practicable,    processes 
should  be  shown  by  means  of  experiments. 

3.  Uses  of  ice  and  vapor  in  nature  and  to  man. 

4.  The  formation  of  clouds,  and  their  kinds. 

5.  How  rain  is  produced  ;  its  uses  or  benefits,  especially 
in  the  growth  of  plants. 

6.  How  springs,  rivulets,  creeks,  rivers,  ponds,  and  lakes 
are  formed. 

REMARK. — If  no  pictures  are  at  hand  that  illustrate  it,  draw- 
ings can  be  made  upon  the  blackboard  to  answer  the  purpose. 

7.  The  uses  of    water  for   drinking,  washing,  cooking, 
highways,  as  a  force,  and  as  a  cooler  and  moistener  of  the 
air. 

3.  Air. — i.  The  properties  of  the  air. 

2.  Its  use  in  supporting  animal  and  vegetable  life. 

3.  How  winds  are  caused,  and  their  kinds. 

4.  The  uses  of   winds  in  carrying  vapor,  purifying  and 
cooling  the  air,  propelling  vessels,  and  turning  machinery. 

5.  Changes  of  temperature,  how  caused,  and  how  meas- 
ured. 

6.  Effects  of  changes  of  temperature  upon   animal   and 
vegetable  life. 

7.  Protection  of  animal  and  vegetable  life  against  great 
changes — summer's  heat  and  winter's  cold. 

4-  Heat. — i.  Its  source  or  modes  of  production, 

2.  Its  effect  upon  different  substances, 

3.  Its  uses. 


176  Science  and  Art  of  Education. 

5»  Plants. — i.  Common  varieties. 

2.  The  roots,  and  the  part  they  perform  in  the  growth  of 
plants. 

3*  The  kinds  of  roots,  also  duration. 

4.  Roots  used  for  food. 

5.  The  kinds  and  use  of  stem. 

6.  Leaves,  their  forms  and  use. 

7.  Flowers,  their  forms,  use,  and  beauty. 

REMARK.— The  children  should  be  trained  to  draw  and 
paint  plants,  including  flowers. 

8.  The  kinds  of   fruit   or  seeds,  when  they  ripen,  and 
their  uses. 

9.  Buds,  what  they  contain,  when  they  begin  to  swell, 
and  why  they  do  so. 

10.  When  the  blossoms  appear. 

11.  When  the  fruit  ripens. 

12.  When  the  leaves  begin  to  fall  and  what  causes  them 
to  fall. 

13.  How  roots  are  protected  from  the  cold  in  the  winter. 

14.  Food  of  plants,  also  cultivation. 

15.  Medicinal  and  food  plants,  also  plants  that  are  poi- 
sonous. 

6.  Domestic  Animals. — i.  Varieties,  also  form  or  struc- 
ture. 

2.  Adaptation  of  structure  to  mode  of  life  and  subsist- 
ence. 

3.  Grass,  grain,  and  flesh  eating  animals,  and  habits  and 
use  of  each. 

4.  How  fed,  sheltered,  and  cared  for. 

7»    Wild  Animals. — i.  Varieties  of  form  or  structure. 

2.  Adaptation  of  structure  to  mode  of  subsistence  and 
defence  or  protection. 

3.  Their  habitat,  or  homes. 

4.  Grass,  grain,  nut,  and  flesh  eating  quadrupeds. 


Suggestions  for  Teaching  Numbers.  177 

(a)  Those  that  are  useful  for  food,  skins,  and  furs, 

(b)  How  captured,  also  how  tamed. 

5.  Flesh  and  grain  eating  birds,  and  varieties  of  each. 

(a)  How  they  fly,  and  how  they  hold  themselves  to  limbs 
of  trees  and  other  objects. 

(b)  How  and  when  they  secure  their  food. 

(c)  How  they  are  captured  ;  also  how  tamed. 
(a)  Which  used  as  food,  and  why. 

6.  Fish,  their  varieties,  also  adaptation  of  structure  to 
medium  in  which  they  live. 

(a)  How  they  move  themselves,  and  adaptation  of  form 
to  mode  of  movement. 

(b)  Their  food,  and  how  they  secure  it. 

(c)  Which  are  used  for  food. 

(d)  Methods  of  catching,  preserving,  and  preparing  for 
the  table. 

Among  animals  should  also  be  included  insects  and  rep- 
tiles, the  latter  embracing  lizards,  turtles,  tortoises,  frogs, 
toads,  and  serpents.  An  examination  and  study  of  the 
nature  and  habits  of  these  will  create  an  interest  in  them 
in  the  children  and  will  lead  them  to  see  that  none  of 
God's  creatures  are  useless,  but  that  all  of  them  when  prop- 
erly understood  have  their  purpose,  and  instead  of  being 
our  enemies  are  our  friends. 

REMARK. — Microscopes  are  necessary  for  some  of  the  work 
referred  to. 

8.  Man. — i.  His  superiority  to  other  orders  of  creation. 

2.  House  and  home  life  in  comparison  with   those  of 
other  living  beings. 

3.  Adaptation   to  a  variety  of    occupations  or  employ- 
ments. 

4.  His  genius  in  using  the  forces  of  nature  in  the  per- 
formance of  labor  and  in  surmounting  obstacles. 

5.  Modes  of  communication  and  travel. 


178  Science  and  Art  of  Education. 

6.  Possibility  and  means  of  improvement. 

7.  Means  or  modes  of  enjoyment. 

8.  Pictures  of   the  various  races  of   the  human   family 
should  be  shown,  and  the  race  characteristics  described. 

9.  The  effect  of  climate  upon  character  and  disposition 
should  be  explained. 

REMARK. — As  before  stated,  the  foregoing  work  should,  as 
far  as  possible,  be  informal  and  conversational. 

9-  Study  from  Maps  and  Models. — i.  After  the  locality  or 
community  in  which  the  children  have  their  homes  has 
been  explored  and  studied  as  carefully  and  thoroughly  as 
their  age  will  permit,  and  a  sufficient  amount  of  experiences 
or  apperceiving  concepts  stored  away  as  constructive  ma- 
terial, the  children  are  prepared  to  extend,  their  vision,  by 
means  of  the  imagination,  to  the  unseen.  This  they  must 
learn  to  do  by  the  use  of  pictures,  maps,  and  models,  and 
the  best  and  most  natural  way  to  learn  to  understand  a  map 
or  a  model  is  to  help  to  make  one.  The  school-room  is  the 
most  convenient  and  suitable  thing  to  begin  with  in  map- 
ping. 

2.  To  enable  the  children  to   judge  of    distances   and 
areas  they  should  have  practice  in  making  measurements. 
A  yard,  rod,  or  mile,  either  linear  or  square,  should  convey 
something  definite  to  them. 

3.  The  cardinal  points — east,  west,  north,  and  south — 
should  be  determined  and  marked  or  fixed  upon  the  floor 
or  elsewhere  by  means  of   lines  connecting  the   opposite 
ones. 

4.  A  map  of  the  school-room  may   be  made  upon  the 
floor,  but  better  upon  a  piece  of  heavy  paper,  say  a  yard 
square,  or  larger,  if  necessary,  painted  with  a  mixture  of 
shell-lac  (dissolved  in  alcohol)  and  lampblack. 

5.  To  make  the  map,  the  paper  should  be  laid  at  some 
convenient  place  upon  the  floor.     If  the  map  is  to  be  pro- 


Suggestions  for  Teaching  Numbers.  179 

portioned  to  the  size  of  the  room — about  an  inch  to  a  foot 
— the  pupils  should  make  the  measurements,  determine  the 
proportions,  and  otherwise  assist  the  teacher  in  the  work. 

Frequent  questions  should  be  asked  of  the  pupils  with 
regard  to  the  direction  of  lines,  the  location  of  seats, 
teacher's  desk,  and  other  objects. 

6.  After  the  map  has  been  made  and  the  pupils  can  read 
it — name  any  object  upon  it  pointed  to  by  the  teacher  or 
one  of  their  own  number,  also  its  direction  from  some  point 
named — it  may  be  hung  upon   the  wall  and  again  read. 
The  latter  reading  will  prevent  the  erroneous  notion  some- 
times formed  by  pupils  that  north  is  in  a  vertical  line  above 
south,  or  at  the  zenith. 

7.  After  the  children  have  become  familiar  with  the  map 
of  the  school-room,  the  surroundings  of  the  school,  and,  if 
in  a  town  or  city,  some  of  the  principal  streets  and  build- 
ings may  be  added.     Next,  if  it  contains  enough  objects  of 
importance,  the  county  may  be  drawn,  then  the  state,  and 
other  states  separately  and  in  sections  or  groups,  until  the 
whole  country  has  been  built  or  mapped,  and  studied,  and 
the  children  can  in  imagination  see  it  or  any  part  of  it. 

8.  As  will  be  noticed,  the  method  here  indicated  is  pro- 
gressive ;  and  to  show  more  definitely  how  it  may  be  carried 
out,  the  following  suggestions  are  added  :  (a)  If  the  school 
is  in  Pennsylvania,  begin  with  that  State  ;  and  if  the  pupils 
have  had  little  or  no  practice  in  drawing  from  memory,  the 
teacher  should  make  the  first  drawing,  explaining  his  work 
as  he  proceeds. 

(b)  For  the  first  lesson,  the  pupils  should  prepare  to  draw 
the  outline  (of  the  state)  and  the  rivers,  and  at  the  recita> 
tion  make  a  sketch  of  their  lesson  upon  the  blackboard, 
and  describe  it,  the  teacher  questioning  them  upon  it. 

(c)  For  the  second  lesson,  they  should  add  to  the  first 
the  mountains,  principal  towns,  cities,  and  other  objects  of 
importance.     After  they  have  completed  their  sketches  or 


1 80  Science  and  Art  of  Education. 

maps  they  should  describe  them,  and  the  teacher  should 
ask  questions  about  the  proportions,  the  relative  position  of 
objects  represented  upon  them,  etc. 

(d)  For  the  third  lesson,  the  second  should  be  repro- 
duced as  a  review,  and  the  outline  and  the  rivers  of  New 
Jersey  added. 

REMARK  i. — While  the  pupils  are  learning  the  maps,  the 
teacher  should,  with  all  the  helps  at  his  command,  such  as 
models,  pictures,  and  descriptions,  enable  them,  in  imagination, 
to  see  the  states  or  countries  of  which  the  maps  are  represen- 
tations. 

2. — Descriptions,  questions,  and  reviews  of  as  many  previous 
lessons  as  may  be  necessary  should  constitute  a  part  of  every 
recitation. 

(e)  The  fourth  lesson  should  review  the  third  and  add  to 
it  the  mountains,  cities,  etc.,  of  New  Jersey. 

(/)  The  fifth  lesson  should  include  the  fourth  and  add 
to  it  Delaware,  with  all  in  it  of  importance. 

(g)  For  the  sixth  lesson,  add  to  the  flfth  the  outlines  of 
Maryland. 

(ti)  For  the  seventh  lesson,  add  to  the  sixth  whatever 
may  be  considered  of  importance  in  Maryland. 

REMARK. — The  daily  reviews  should  be  spirited  ;  slow,  sleepy 
work  should  not  be  permitted.  The  pupils  should  be  trained 
to  accurate  rapid  sketching  or  mapping. 

(/)  If  by  this  time  the  pupils  have  Pennsylvania  well 
pictured  in  their  minds,  so  that  they  can  make  a  rapid  and 
sufficiently  accurate  sketch  of  it  and  describe  it,  they  may 
drop  that  state  for  a  while  and  add  to  the  others  already 
drawn  Virginia,  then  West  Virginia,  and  so  on,  always,  in 
the  sketching,  dropping  those  first  made  as  soon  as  they  are 
well  fixed  in,  the  mind. 

(J)  A  daily  review,  either  oral  or  by  sketching,  is  a  neces- 
sity, in  order  to  connect  the  work  from  the  beginning  into 
a  mental  picture  of  the  whole  and  to  impress  it  firmly  upon 
the  mind.  Frequently  all  the  states  that  have  been  studied 


Suggestions  for  Teaching  Numbers.  181 

should  be  sketched  as  a  whole.  It  is  of  far  more  impor- 
tance that  what  has  been  learned  should  find  a  permanent 
lodgment  in  the  mind,  than  that  more  should  be  added  to 
what  is  already  fading. 

(k)  After  New  Jersey  has  been  added  to  Pennsylvania, 
instead  of  taking  Delaware  next,  New  York  may  be  taken, 
then  Connecticut,  Rhode  Island,  Massachusetts,  Vermont, 
New  Hampshire,  and  Maine. 

REMARK. — If  the  pupils  can  do  so,  they  may  group  two, 
three,  or  more  states  together  as  a  lesson. 

(/)  The  teacher  should  begin  with  the  state  in  which  his 
school  is  located  and  build  from  that  out.  He  may,  of 
course,  begin  with  some  other  state,  but  it  is  more  natural 
to  begin  at  home. 

(///)  Only  things  that  are  important  should  be  found  in 
the  sketches. 

(//)  Maps  in  which  no  exactness  is  required  should  be 
proportioned  by  the  eye,  without  construction-lines.  How- 
ever, if  a  pupil  finds  it  difficult  to  give  the  desired  shape  to 
his  map  while  preparing  his  lesson  for  a  blackboard  sketch, 
dividing  his  paper  into  rectangles,  proportioned  as  nearly  as 
possible  to  those  made  by  the  parallels  and  meridians  of 
the  maps  in  his  book,  will  give  him  all  the  points  he  needs 
for  the  required  form. 

(o)  While  the  pupils  are  doing  the  work  here  suggested 
they  should  also  read  the  descriptive  matter  found  in  their 
books  pertaining  to  the  states  which  they  are  sketching, 
and  should  be  questioned  upon  it  by  the  teacher.  What- 
ever of  this  matter  may  be  considered  of  sufficient  impor- 
tance to  constitute  a  permanent  possession  of  the  mind 
should  also  enter  into  the  daily  reviews. 

(p)  Climate  and  productions  are  not  limited  by  political 
divisions,  but  belong  to  physical  sections  or  regions,  and, 
unless  peculiar  to  a  state,  should  be  taught  with  the  regions 
to  which  they  belong. 


182  Science  and  Art  of  Education. 

(q\  Definitions,  instead  of  being  the  first  thing  presented 
to  a  learner,  should  generally  be  the  last,  and  instead  of 
being  memorized  from  a  book  should  as  far  as  possible  be 
drawn  from  examples  or  given  from  a  knowledge  of  the 
subject. 

(r)  To  complete  the  map  of  North  America,  add  to  the 
United  States  the  British  possessions,  Alaska,  and  Green- 
land, on  the  north,  and  Mexico,  Central  America,  and  the 
West  Indies,  on  the  south,  grouping  all  into  one  picture. 

REMARK. — Countries  of  which  our  knowledge  is  limited  and, 
at  best,  inaccurate,  should  have  only  the  outline,  principal  di- 
visions, rivers,  mountains,  and  cities  represented  on  the  map. 

(s)  South  America  may  follow  North  America,  then 
Africa,  Europe,  Asia,  with  its  surrounding  islands,  Australia, 
and  the  more  important  islands  of  the  Pacific  Ocean. 

9.  After  a  whole  country  has  been  mapped  and  impressed 
upon  the  minds  of  [the  pupils,  its  prominent  or  controlling 
physical  features — those  upon  which  the  climate,  produc- 
tions, etc.,  depend— should  be  studied  on  a  relief  map  or 
on  a  model  in  sand. 

10.  The  study  of  the  influence  of  the  physical  features  of 
a  country  should  be  followed  by  the  position  of  the  country 
upon  the  globe,  also  its  position  with  reference  to  other 
countries;  and  its  intellectual,  moral,  and  commercial  posi- 
tion or  standing  among  the  countries  of  the  earth. 

11.  Countries  should  also  be  compared  with  each  other, — 
their  resemblances  and  contrasts  noted, — as  indicated  in 
Part  II,  under  Association. 

12.  When  each  country  has  its  place  assigned  upon  the 
globe,  and  a  picture  of  the  whole  has  been  formed  in  the 
minds  of  the  pupils,  then  they  are  prepared  to  study  it  in- 
telligently as  a  whole,  with  its  lands,  waters,  motions,  forces 
operative  upon  it,  diversities,  and  possibilities  of  life,  etc. 
This  is  a  study  of  cause  and  effect,  and  suitable  only  for 


Suggestions  for  Teaching  Numbers.  1 83 

pupils  of  sufficient  age  and  mental  development  to  make 
broad  generalizations; 

10.  The  Sand-box. — i.   Elevations  are  best  represented  by 
means  of  models  of  sand,  clay,   putty,   or  paper  pulp.     A 
box  of  inch  pine-boards,  3  ft.  X  4  ft.  X  3  in.,  painted  on 
the  inside  with  two   or  three   thick  coats  of  lead  paint, 
placed  upon  trestles  2  ft.  in  height  and  containing  about  a 
peck  or  ten  quarts  of  moulders'  sand  obtained  at  a  foundry, 
is  not  expensive,  and   should  be  found  in  every  school  in 
which  geography  is  taught. 

2.  That  the  sand  may  at  all  times  be  ready  for  use,  it 
should,  when  not  needed,  be  kept  in  a  rounded  heap, 
pounded  together  to  hold  the  moisture,  and  once  a  day,  or 
oftener,  sprinkled  with  as  much  water  with  a  sprinkling- 
can  as  will  soak  in  without  running  off. 

11.  Relief -maps. — i.  Instead    of    purchasing    expensive 
relief-maps,  every  teacher  can,  with  the  assistance  of  his 
pupils,  make  his  own  maps  of  paper  pulp.     The  pulp  may 
be  made  in  the  following  manner  :  Take  white  waste  paper, 
(other  paper  may  be  used)  and  tear  it  into  pieces  about  an 
inch  square,  until  enough  has  been  prepared  to  fill  a  com- 
mon-sized wooden  water-pail  or  bucket.     Pour  enough  hot 
water  upon  the  paper  to  cover  it  two  or  three  inches  deep, 
and  let  it  remain  on  it  six  or  eight  hours,  or  overnight.    When 
ready  to  make  the  pulp,  pour  nearly  all  the  water  off,  leav- 
ing only  as  much  as  may  be  necessary  for  the  proper  moist- 
ure of  the  pulp.     Pour  a  quart  or  more  (if  the  pail  is  nearly 
full  of  paper)  of  flour  starch  upon  the  paper,  and  work  or 
mix  it  well  in  with  the  hands.     Now,  after  pouring  half  the 
mass  into  another  vessel, — the  reduction  being  more  easily 
and  quickly  made  by  taking  a  half-pailful  at  a  time, — let 
each  of  three  boys  take  in  each  hand  a  stick  of  hard  wood 
about  three  feet  long,  three-fourths  of  an  inch  thick,  and 
pointed  at  one  end,  and,  sitting  around  the  pail,  drive  them 
down  through  the  mass  as  rapidly  as  possible  (frequently 


Science  and  Art  of  Education. 


stirring  the  paper  up  from  the  bottom),  until  the  desired 
condition  of  the  pulp  has  been  attained.  Treat  the  other 
half  in  the  same  manner,  and  when  the  pulp  has  all  been 
made,  put  it  into  a  stone  jar  or  crock,  and  cover  it  well,  in 
order  that  it  may  hold  the  moisture  until  it  is  wanted  to 
make  the  maps. 

2.  To  make  the  maps,  take  a  piece  of  cardboard  about 
an  eighth  of  an  inch  in  thickness,  proportion  the  map  to  the 
one  in  the  book  used  as  a  copy,  making  it  two,  two  and  a 
half,  three,  or  four  times  the  size  of  the  copy.     Cut  the  card 
at  least  two  inches  larger  each  way  than  the  proposed  map, 
to  allow  for  an  inch  border  all  around.     Next,  draw  the 
map  upon  the  card,  and  when  done,  with  the -fingers  put 
the  pulp  on,  not  thicker  than  an  eighth  of  an  inch,  pressing 
it  down  well  to  make  it  adhere  to  the  card.     It  is  best  to 
begin  putting  on  the  pulp  around  the  outline,  and  after- 
wards to  cover  the  remainder.     No  pulp  should  be  put  upon 
places  intended  to  represent  lakes,  nor  should  rivers  be 
covered  with  it.     Simply  press  the  pulp  down  on  both  sides 
against  the  river  line,  but  not  together,  and  when  it  dries  it 
will  sepatate  along  the  line  and  represent  the  river. 

3.  The  maps  can  be  made  harder  and  more  durable  if, 
when  dry,  they  are  given  a  coat  of  gum-arabic.     If  desired, 
when  the  gum-arabic  is  dry  the  maps  may  be  painted. 

4.  To  make  the  pulp  adhere  more  firmly  to  the  card- 
board, the  latter  should  also  be  given  a  coat  of  mucilage 
inside  of  the  outline.     If  this  is  done  the  mucilage  should 
be  allowed  to  dry  before  the  pulp  is  put  on. 


HISTORY. 

1.  History  is  a  record  of  human  deeds,  either  of  individ- 
uals or  communities  ;  and  since  deeds,  measured  by  moral 
standards,  may  be  good  or  bad,  the  sfudy  of  history  is  the 
study  of  conduct,  the  study  of  morals.      Viewed  in  this 
light  it  has  an  important  bearing  upon  the  formation  or 
growth  of  character. 

2.  The  greater  the  age  a  country  has  attained  the  larger 
its  accumulation  of  historical  matter  at  the  command  of  the 
teacher.     In  wealth  of  material,  it  is  true,  the  lands  beyond 
the    ocean    surpass    us ;    but    for    the  lessons   that   young 
Americans  need  to  learn,  our  stores  are  not  only  ample,  but 
superior  to  all  others.     Our  soil  has  been  consecrated  to 
liberty.     The  heritage  which  our  forefathers  have  left  us  is 
priceless.     No  other  country  upon   the  globe  offers  such 
opportunities  for  persons  of  ambition   and  worth  to  rise 
from  the  humblest  walks  in  life  to  the  highest.     No  law 
says,  "  thus  far  shalt  thou  go  but  no  further." 

3.  But  those  who  are  soon  to  become  actors  in  the  drama 
of  life  must  not  only  be  taught  to  appreciate  the  value  of 
the  freedom  handed  down  to  them,  but,  above  all,  how  to 
maintain  it  ;  they  must  be  taught  that  "  righteousness  "  in 
the  individuals    "exalts  a   nation,"   and  that  sin  is   a   re- 
proach  to  any  people.     That   character   or   worth   makes 
the  man  must  therefore  be  impressed  upon  the  minds  of 
the  children  so  as  to  become  the  ruling  principle  of  their 
conduct  and  lives  ;  and,  to  accomplish  this  end,  no  other 
branch  of  study  furnishes  material  equal  to  that  of  history. 

185 


1 86  Science  dnd  Art  of  Education. 

4.  Erroneous  notions  concerning  the  influence  of  certain 
kinds   of  matter   prevail    among    teachers.     For   example, 
some  labor  under  the  delusion  that  the  study  of  battles  and 
bloodshed  cultivates   a  spirit  of   patriotism  and  bravery. 
They    do   not   distinguish    between    bloodthirstiness,   and 
patriotism  and  bravery.     Pupils  nourished  with  the  former 
diet — soon  eagerly  devoured  by  boys— frequently  find  the 
ordinary  quiet  walks  of  life  too  uneventful  for  "  the  fires 
that  in  them  burn,"  and  start  on  a  career  of  lawlessness. 
The  matter  for  class  use  for  children  should  therefore  be 
selected  with  care. 

5.  Children  should  be  taught,  and  early,  too,  that  might 
does  not  make  right  in  the  eyes  of  the  civilized  world  ;  and 
that,  consequently,   decisions   rendered   by   the    sword — a 
relic   of  barbarous   ages — are   not   to   be   relied   upon   as 
founded   upon   justice,  nor  as  compatible  with    Christian 
civilization. 

6.  We  look  to  the  past  also  for  guidance  in  the  future. 
For  this  purpose,  however,  much  of  the  past  is  not  only  un- 
necessary, but  useless  ;  hence  teachers  of  history  should 
exercise  more  judgment  than  is  usually  done  in  selecting 
that  which  has  a  direct  bearing  upon  the  points  they  are 
endeavoring  to  have  brought  out  or  discussed.     When  the 
pupils  have  reached  a  sufficient  age  and  stage  of  mental 
development  to  do  so,  the  selection  of  the  matter  should,  as 
far  as  possible,  be  left  to  the  exercise  of  their  own  judg- 
ment, the  teacher  simply  stating  the  question  to  be  dis- 
cussed. 

REMARK. — A  teacher  of  history  should  be  free  from  all  taint 
of  political  bias.  A  politician  or  partisan  would  on  all  occa- 
sions that  offered  themselves  try  to  influence  his  pupils  to 
become  of  his  own  sort,  and  thus  defeat  the  object  of  the  study. 

7.  When  not  confined  to  the  dry  boxes  of  the  subject, 
such  as  uneventful  administrations  and  the  like,  or  to  the 
packing  of  the  memory  with  dates  and  less  important  facts, 


Suggestions  for  Teaching  Numbers.  187 

and  when  taught  intelligently,  history  is  a  study  of  infer- 
ence, induction,  one  of  the  best  thought,  or  logical,  subjects, 
and  should  not  fail  to  be  intensely  interesting. 

8.  A  teacher  of  history  should  be  a  good  story-teller. 
He  should  be  able  to  put  dry  facts  into  the  form  of  stories 
and  invest  them  with  interest.    Children  are  fond  of  stories, 
hence  this  is  the  best  way  of  presenting  the  subject  to  them. 

9.  If  the  formation  of  Christian  characters  is  uppermost 
in  the  teacher's  mind  and  his  pupils  are  primarians,  he  can 
do  nothing  better  than  begin  with  Bible  stories,  those  of 
the   Old   Testament,    of   Abraham,    Isaac,    Jacob,    Joseph, 
Moses,    Joshua,     Samuel,    Solomon,    David,    Elisha,    Job, 
Isaiah,    Jeremiah,    Daniel,    and,    in   the    New   Testament, 
Christ,  whose  life  and  teachings  furnish   endless  material 
for  building  character. 

10.  Following  Bible  stories  may  come  the  history  of  our 
own  country,  beginning  with  that  of  the  community — town- 
ship or  county — in  which  the  school  is  located,  bringing  in 
the   Indians,    then    the   discovery   and   settlement   of   the 
country  by  Europeans,  the  encroachment  of  the  white  man 
upon   the   hunting-grounds  of   the    Indians,   the   resulting 
animosities  and  strifes,  etc.     Special  stress  should  be  laid 
upon  the  events  and  influences  that  have  controlled  our 
growth  and  strength  as  a  nation. 

11.  With  whatever  matter  the  teacher  may  begin,  whether 
Bible  stories  or  the  community,  it  should  be  given  in  the 
form  of  anecdotes  and  stories.     No  books  should  be  used  ; 
for  there  is  no  surer  way  to  destroy  interest  in  the  subject 
and  create  a  dislike  for  it  than  requiring  the  contents  of 
books  to  be  recited.     However,  when  pupils  are  old  enough 
to  read  understandingly  they  should  be  encouraged  to  con- 
sult books,  and  if  the  instructions  they  have  received  from 
the  lips  of  the  teacher  have  created  the  proper  interest, 
they  will  gladly  avail  themselves  of  every  opportunity  to 
add  to  their  stock  of  knowledge. 


1 88  Science  and  Art  of  Education. 

12.  The  matter  for  advanced  pupils  should  frequently,  if 
not  generally,  be  given  in  the  form  of  problems,  or  subjects 
for  discussion,  to  give  them  practice  in  solving  the  perplex- 
ing problems  that  will  meet  them  later  in  life  and  which 
confront  the  citizens  of  a  country  like  ours. 

13.  Teachers  of  history  should  bear  in  mind  that  a  good 
knowledge  of  their  subject  of  instruction  does  not  neces- 
sarily imply  a  large  accumulation  of  facts,  but  the  ability 
to  use  those  at  command  to  the  best  advantage. 

14.  A  teacher  of  history  should  have  all  the  appliances 
in  the  way  of  maps,  charts,  pictures,  etc.,  that  are  neces- 
sary to  give  his  pupils  accurate  and  clear  mental  pictures 
of  the  events  that  present  themselves  in  their  lessons.     It 
is  more  frequently  on  account  of  failures  in  imagining  than 
of  treachery  of  memory  that   lessons  are  unsatisfactorily 
prepared.     The  more  real  the  teacher  succeeds  in  making 
his  instructions  the  better  they  will  be  comprehended  and 
remembered. 

15.  In  history  fully  as  much  as  in  anything  else,  if  not 
more  so,  daily  reviews  constitute  a  necessity.     This  is  the 
only  way  to  connect  the  work  and  to  give  it  a  permanent 
place  in  the  mind. 


part  ?3I3J. 

THE  HUMAN  BODY. 

1.  Of  all  the  studies  pursued  in  the  schools,  that  relating 
to  the  knowledge  and  care  of  our  bodies  is  least  under- 
stood.    It  is  perfectly  safe  to  say  that  we  do  not  under- 
stand how  to  live  well,  and  the  little  we  pretend  to  know  we 
disregard. 

2.  Our  food  is  selected  in  almost  total  indifference  of 
what  the  system  craves  in  kind,  proportion,  and  quantity. 
Some  kinds  come  too  frequently,  others  the  reverse.    Again, 
some  that  the  system  does  not  need,  cannot  use,  and  that 
therefore  do  harm,  are  provided,  while  others  that  are  needed 
are  not  supplied.     Neither  the  work   performed  nor  the 
season  is  consulted.     The  same  kind  is  frequently  provided 
for  all,  whether  suitable  or  unsuitable,  whether  their  stom- 
achs can  bear  it  or  not.     All  are  supposed  to  be  alike. 

3.  Cooking  is  done  by  persons  who  are  ignorant  of  the 
laws  of  health  ;  frequently  they  do  not  know  that  there  are 
such  laws  ;   and,  in  the  preparation,  either  destroy  the  most 
nutritious  part  of  the  food  or  permit  it  to  evaporate. 

4.  The  amount  of  exercise  needed  is  as  little  understood 
as  the  food  required.     Either  too  much  is  taken  or  not 
enough.     It  is  scarcely  known,  and  still  less  believed,  that 
the  human  machine,  like  others  not  human,  may  be  run  too 
fast  or  too  slow  ;  neither  of  which  can  long  be  done  with 
impunity.     The  avenger  invariably  comes  to  call  a  halt. 

5.  Rest,  in  the  form  of  sleep,  seems  to  be, too  much  re- 

189 


1 90  Science  and  Art  of  Education. 

garded  as  a  thing  that  can  be  put  off  from  time  to  time 
until  there  is  nothing  else  to  do  ;  but  rest  is  fully  as  impor- 
tant as  food,  and  while  some  may  take  so  much  as  to  be- 
come tired  of  it,  others,  and  many  of  them,  do  not  take 
enough,  especially  those  who  sleep  by  the  clock  and  not  by 
what  they  need.  Fortunately,  no  one  needs  a  clock  to  tell 
him  when  he  has  had  enough  ;  he  has  his  guage  within  him. 
Those  who  claim,  as  some  do,  that  time  does  not  permit 
them  to  sleep  until  they  feel  that  they  have  had  sufficient, 
earlier  or  later  pay  the  penalty  for  their  indiscretion  or 
imprudence. 

6.  Cleanliness  of  person  is  also  a  thing  that  needs  more 
attention  than  it  usually  receives.     Bathing,  some   think, 
should  be  done  now  and  then,  say  once  a  week  or  month, 
just  as  there  may  be  time  to  spare  from  other  duties.     But 
daily  bathing,  and  during  warm  weather  more  frequent,  is 
a  necessity  to  comfort  and  health.     The  pores  of  the  skin 
need  to  be  kept  open  and  active. 

7.  Ventilation  is  seldom   overdone,  but  in   ninety-nine 
cases  in  a  hundred  the  reverse.     Pure  air,  if  a  little  cool,  is 
considered  dangerous,  while  the  rankest  poison  thrown  off 

•  from  the  lungs  and  skin  is,  with  the  utmost  composure  and 
ignorance,  time  and  again  returned  to  the  lungs,  until 
almost  complete  stupor  ensues. 

8.  What  are  our  schools  doing  to  remedy'these  defects  ? 
What   are  they   doing  to  teach   right  living — well  living  ? 
Will  memorizing  the  names  and  number  of  the  bones,  teeth, 
muscles,  nerves,  etc.,  usher  in  the  wished-for  millennium  ? 
If  it  is  supposed   to  do  so,  it  has  hitherto  proved  a  signal 
failure  ;  and   as  the  past  has  bee.n  so  will  the  future  be, 
unless  a  wiser  course  be  pursued. 

9.  It  is  not  unfair  to  ask,  how  many  persons  who  under- 
take to  give  instruction   in  this  all-important  subject  are 
competent  to  do  so?     Not  a  few  of  them,  judging  from 
their  frequent' ailments,  dp  not  know  their  own  bodies  we!! 


Suggestions  for  Teaching  Numbers.  191 

enough  to  take  care  of  them,  yet  do  not  hesitate  to  instruct 
others  ho\v  to  take  care  of  theirs. 

10.  The  structure  of  the  body  is  well  enough  understood 
to  be  taught  with  success.     All  that  teachers  need  is  to 
make  themselves  thoroughly  acquainted  with  it. 

1 1.  With  regard  to  hygiene  the  case  is  different.     All  that 
can  be  learned  from  books  and  teachers  in  the  present  state 
of  knowledge  of  the  subject   is  some  very  general  facts, 
nothing  more.     Until  we  shall  have  something  much  more 
definite  than  we  now  possess,  and  perhaps  ever  after,  every 
one  must  study  himself  to  learn  what  his  well-being  de- 
mands.    This  study  must  be  inductive,  and   must  deter- 
mine  what,    under   varying    conditions,    is   healthful   and 
what  injurious. 

12.  Primary  pupils  should,  as  far  as  possible,  be  taught 
objectively,  without  the  use   of  books.     One  of  the  best 
teachers'   helps   for  giving  such    instruction   is   "  Practical 
Work   in    the   School-room,"    Part  I — The  Human  Body, 
published  by  A.  Lovell  &  Co.,  New  York.     Lessons  on  The 
Boy,  in  "  Systematic   Science   Teaching,"  a  recent  work, 
published  by  D.  Appleton  &  Co.,  New  York,  will  be  found 
exceedingly  helpful  in  showing   how   such   and  all  other 
science  instruction  should  be  given. 

13.  For  work  above  the  primary  classes  the  following  or- 
der of   presenting  the  subject  may  be  followed  :  i.  The 
framework  or  bones  ;   2.  The  muscles  ;  3.  The  skin  ;  4.  Di- 
gestion ;  5.  Food  ;  6.  Circulation  ;  7.  Respiration  ;  8.  The 
nervous  system  ;  9.  The  senses. 

REMARK.— In  connection  with  each  part  or  organ   should 
also  be  taught,  as  far  as  possible  or  practicable,  its  care. 

14.  All  unimportant  and  unnecessary  details  and  scientific 
terms — a  burden  to  the  memory — should  be  omitted.     It  is 
more  important  that  pupils  should  become  interested  in  the 
study  of  their  own  bodies  than  that  they  should  know  all 


192  Science  and  Art  of  Education. 


about  it.     The  orcler  of  presentation  should  generally  be, 
first  the  thing,  then  its  name. 

15.  To  teach  the  human  body  successfully,  either  a  skel- 
eton and  models  of  the  various  organs  are  required  or  a 
manikin  ;  without  either  of  these  it  is  impossible  to  give 
the  pupils  an  accurate  conception  of  the  forms  and  position 
of  the  internal  organs. 


CIVIL  GOVERNMENT. 

1.  There  is  no  reason  why  the  children  in   the   lower 
grades  of  schools  should  not  be  made  acquainted  with  the 
elements  of  civil  government.     There  is  nothing  difficult  to 
understand  about  the  subject,  and  if  presented  in  an  intelli- 
gent manner  it  is  an  interesting  one. 

2.  The  first  lessons  should  be  about  their  own  community, 
whether  township  or  borough,  and  should  include  the  fol- 
lowing:  i.  What  public  duties  arc,  and  why  public  rather 
than  private  ;  2.  By  what  officers  the  duties  are  performed; 
3.  Whether  officers  are  elected  or  appointed,  and  by  whom, 
how,  when,  and  for  what  length  of  term  ;  4.  How  officers 
are  installed,  and  when  ;  5.  How  and  by  whom  paid  ;  6. 
Duties  each  is  required  to  perform  ;  7.  Rights  and  duties 
of   citizens  ;  8.  How   rights   are   secured   and   wrongs  re- 
dressed ;  9.  What  laws  are,  by  whom  made,  for  whose  ben- 
efit, and  why  needed  ;  10.  What  the  laws  forbid. 

Next  should  come  the  government  of  the  county,  and 
then  as  much  of  that  of  the  State  as  the  pupils  are  old 
enough  to  understand  and  to  be  interested  in. 

3.  No  subject  should  be  presented  to  pupils  before  they 
have  reached  a  period  of  life  at  which  they  can  be  inter- 
ested in  it ;   hence  the  study  of  the  general  government 
should  be  left  for  the  high-school. 

193 


DRAWING. 

Drawing  is  a  mode  of  expression  that  manifests  itself 
early  in  children.  Give  one  a  pencil  or  a  piece  of  crayon 
and  he  will  try  to  express  something,  however  crude  or  un- 
intelligible the  performance  may  be.  Since  the  desire  or 
instinct  exists,  why  not  foster  it  ?  What  the  children  need 
at  this  period  is  encouragement,  help.  Hence,  whenever 
anything  presents  itself  in  their  lessons  that  admits  of  rep- 
resentation by  lines  or  colors,  let  them  try  to  draw  it  or 
paint  it ;  and,  when  necessary,  show  them  how  to  improve 
their  work.  If  this  course  be  pursued,  drawing  and  paint- 
ing will  be  taught  in  the  most  natural  way,  and  without  a 
special  class  or  period  for  it 

'95 


NEW  BOOKS  FOR  TEACHERS. 

ILES'  A  CLASS  IN  GEOMETRY. 

By  GEORGE  ILES.  "It cannot  fail  to  give  to  the teachei 
of  this  science  new  enthusiasm  and  new  ideas,  and  to 
all  teachers  the  pleasure  arising  from  following  our 
ideal  method."  Limp  cloth.  Price  300.  post-paid. 

KELLOGG'S  ELEMENTARY  PSYCHOLOGY. 

By  AMOS  M.  KELLOGG,  Editor  of  the  School  journal. 
A  concise  outline  for  Normal  students  and  the  home 
study  of  pedagogy.  It  will  aid  those  who  have  found 
other  works  obscure.  Limp  cloth.  Price  2jc.  post- 
paid. 

ROOFER'S   APPERCEPTION, 

or,  "A  Pot  of  Green  Feathers,"  is  a  very  simple  book 
on  psychology,  strange  as  the  title  may  seem.  It  dis- 
cusses perception  and  shows  how  it  becomes  percep- 
tion. Limp  cloth.  Price  2$c.  post-paid. 

ROOPER'S  OBJECT  TEACHING 

makes  plain  this  much-talked-of  but  little-understood 
subject  both  in  its  philosophical  basis  and  its  practice. 
Limp  cloth.  Price  2<$c.  post-paid. 

HALL'S  CONTENTS   OF  CHILDREN'S  MINDS 

on  Entering  School,  by  G.  STANLEY  HALL,  President  of 
Clark  University,  gives  the  results  of  careful  investiga- 
tions made  by  the  writer  and  others  to  determine  the 
amount  and  kind  of  knowledge  possessed  by  the 
average  child  on  entering  school.  Limp  cloth. 
Price  250.  post-paid. 

#%  Large  descriptive  catalogue  of  Jive  hundred  books  and  aids  fot 
teachers  in  all  branches  of  school  work  free. 

E.  L.  KELLOQQ  &  CO.,  New  York  and  Chicago. 


The  Best  Educational  Periodicals. 


THE  SCHOOL  JOURNAL 

is  published  weekly  at  $2.50  a  year  and  is  in  its  23rd  jear. 
It  is  the  oldest,  best  known  and  widest  circulated  educational 
weekly  in  the  U.  S.  THE  JOURNAL  is  filled  with  ideas  that  will 
surely  advance  the  teachers'  conception  of  education.  The  best 
brain  work  on  the  work  of  professional  teaching  is  found  in  U 
— not  theoretical  essays,  nor  pieces  scissored  out  of  othe* 
journals — THE  SCHOOL  JOURNAL  has  its  own  special  writers—, 
the  ablest  in  the  world. 

THE  PRIMARY  SCHOOL  ° 

is  published  monthly  from  September  to  June  at  $1.00  a  yean 
It  is  the  ideal  paper  for  primary  teachers,  being  devoted  almost 
exclusively  to  original  primary  methods  and  devices.  Several 
entirely  new  features  this  year  of  great  value. 

THE  TEACHERS'  INSTITUTE 

is  published  monthly,  at  $1.00  a  year.  It  is  edited  in  the  same 
spirit  and  from  the  same  standpoint  as  THE  JOURNAL,  and  has 
ever  since  it  was  started  in  1878  been  the  most  popular  educa- 
tionalmonthly  published \  circulating  in  every  state.  Every  lino 
is  to  the  point  It  is  finely  printed  and  crowded  with  illustra- 
tions made  specially  for  it.  Every  study  taught  by  the  teacher 
is  covered  in  each  issue. 

EDUCATIONAL  FOUNDATIONS. 

This  is  not  a  paper,  but  a  series  of  small  monthly  volumes 
that  bear  on  Professional  Teaching.  It  is  useful  for  those  who 
want  to  study  the  foundations  of  education  ;  for  Normal  Schools, 
Training  Classes,  Teachers'  Institutes  and  individual  teachers. 
If  you  desire  to  teach  professionally  you  will  want  it.  Hand* 
some  paper  covers,  64pp.  each  month.  The  History,  Sciencef 
Methods,  and  Civics  of  education  are  discussed  each  month, 
and  it  also  contains  ail  of  the  N.  Y.  State  Examination  Ques- 
tions and  Answers. 

OUR  TIMES 

gives  a  resume  of  the  important  news  of  the  month—not  the 
murders,  the  scandals,  etc.,  but  the  news  that  bears  upon  the 
progress  of  the  world  and  specially  written  for  the  school- room, 
It  is  the  brightest  and  best  edited  paper  of  current  events  pub- 
lished, and  so  cheap  that  it  can  be  afforded  by  every  pupil. 
-  Club  rates,  25  cents. 

%*  Select  the  paper  suited  to  your  needs  and  send  for  a  free  sample. 
Samples  of  all  the  papers  25  cents.  *» 

B.  L.  KELLOGG  &  CO. ,  New  York  and  Chicago. 


BEST  BOOKS  FOR  TEACHERS, 

Classified  List  under  Subjects. 

To  aid  teachers  to  procure  the  books  best  suited  to  their  purpose,  we 
£i ve  below  a  list  of  our  publications  classified  under  subjects.  The  division 
\s  sometimes  a  difficult  one  to  make,  so  that  we  have  in  many  cases  placed 
the  same  book  under  several  titles;  for  instance,  Currie's  Early  Education 
appears  under  PRINCIPLES  AND  PRACTICE  OF  EDUCATION,  and  also 
PRIMARY  EDUCATION.  Kecent  books  are  starred,  thus  * 


HISTOEY  OF  EDUCATION,  GREAT  EDU- 
CATORS, ETC. 

Allen's  Historic  Outlines  ot  Education,       -      - 
Autobiography  of  Froebel, 
browning's  Aspects  ot  Education   Bwt  edition. 
"  Educational  Theories,    Best  edition. 

*  EDUCATIONAL  FOUNDATIONS,  bound  vol.  '91-'92, 
»»  "  "          '" 


Kellogg's  Life  of  Pestalozzi,         - 

Lang's    Comenius,         ------ 

Basedow,    ------- 

Rousseau  and  his  "Emile"  -  -  - 

*  **        Hoi-ace  Mann,  ------ 

*  "        G  reat  Teachers  of  Four  Centuries,       - 

*  •»       Herbart  and  His  Outlines  of  the  Science 

of  Education.       - 
Phelps'  Life  of  David  P.  Page,      - 
Quick's  Educational  Reformers,  Best  edition.  ~ 
*Reinhart's  History  ot  Education,       - 


Retail. 

paper 

cl. 

cloth 

cl. 
paper 

cl. 

paper 
paper 
paper 
paper 
pacer 


Cl.       .25 


PRINCIPLES  OF  EDUCATION. 


pd. 


Our  By 
Price  to  Mail 
Teachers  Extra 

.15 
50        .40 

.25     .20 

,50  .40 
.60 
l.OO 
.15 
.15 
.15 


.05 
pd. 
pd. 
pd. 
pd. 
pd. 

.15     pd. 
.15      pd. 
.25       .20       .03 


.20  .03 

paper              .15  pd. 

cl.     J.OO       .80  .08 

cl.       .25       .20  .03 


Carter's  Artificial  Stupidity  in  School,       -      -     paper 

.15 

pd. 

*EUUCATIONAL  FODN  CATIONS,  bound  vol.  '91-'92,  paper 

.60 

pd. 

*          "                          "                       "          '92-'93,      cl. 

l.OO 

pd. 

Fitch's  Improvement  in  Teaching,      -                    paper 
*Hall  (G.  S.)  Contents  of  Children's  Minds,        -          cl. 

.25 

.15 

pd. 
.03 

Huntington's  Unconscious  Tuition,  -                      paper 
Payne's  Lectures  on  Science  and  Art  of  Education,    cl. 
Reinhart's  Principles  ot  Education,    -                          cl. 

1.00 
.25 

.15 

.80 
.20 

pd. 
.08 
.03 

*>pencer's  Education.    Best,  edition.    -       -       -          cl. 

1.00 

.80 

.10 

Perez's  First  Three  Years  of  Childhood,    -       -          cl. 

1.50 

1.2O 

.10 

*llein*s  Outlines  of  Pedagogics,           -                          cl. 

.75 

.60 

.08 

Tau«'s  Philosophy  of  Education.    Best  edition.  -         cl. 

1.50 

1.2O 

.10 

*Teachers'  Manual  Senes.     24  nos.  ready,     each,  paper 

.15 

pd. 

PSYCHOLOGY  AND  EDUCATION. 

Allen's  Mind  Studies  for  Young  Teachers,        -          cl. 

.50 

.40 

.05 

A  lien's  Temperament  in  Education,  -       -       -          cl. 

.50 

.40 

.05 

*Kelloj.'g's  Outlines  of  Psychology,      ...      paper 
Perez's"  Kirst  Three  Years  oi  Childhood.  Best  edition,  cl. 

.25 

1.50 

.20 
1.2O 

03. 
.10 

Hooper's  Apperception,    Best  edition.       -      -         cl. 
Welch's  Teachers'  Psychology,    -                                 el. 
Tniks  on  Psychology,    -                               cl. 

.25 
1.25 
.MJ 

.20 
l.OO 
.40 

.03 
.10 

.U6 

MANUAL  TRAINING. 

Butler's  Argument  for  Manual  Training,  -      -     paper  .15  pd. 

"Larsaon's  Text-Book  of  Sloyd,  -      -      -      -          cl.     1.50  1.2O  \15 

Love's  Industrial  Education,       -                                c\     1.50  1.2O  J2 

nipham's  Fifty  Lessons  in  Woodworking,        -          cL       .50  .40  .05 

QUESTION  BOOKS  FOB  TEACHERS. 

Analytical  Question  Series.    Geography,  -      -         cl.      .50  .40  .05 

8                 "           "         P. 8.  History,        -         cl.     *.50  .40  .05 

*»                 •*           *4        Grammar,      -      -          cl.       .50  .40  .05 

*  EDUCATIONAL  FOUNDATIONS,  bound  vol.  *91-193,  paper  .60  pd. 

*  "                                       •                  »92.'93.      cl.  l.oo  pd. 


N.  Y.  State  Examination  Quest  ons,   -                        CL  1.00      .80  .08 

*Shaw  's  National  Question  Book   Newly  revised.  1.75  pd. 

Soutbwick's  Handy  Helps,  -----          cl.  1.00       .80  .08 

Southwick's  Quiz  Manual  of  Teaching.  Best  edttion.  cl.  .75      .60  .05 

PHYSICAL  EDUCATION  and  SCHOOL  HYGIENE. 

Groff  's  School  Hygiene,         -                                  paper  .15  pd. 

MISCELLANEOUS. 


Blaikie  On  Self  Culture,       -      -      -      -      - 
Fitch's  Improvement  in  Education,     - 
Gardner's  Town  and  Country  School  Buildings, 
Lubbock's  Best  100  Books,    -      -      -      -      - 

cL 

pacT 

paper 
cl. 

oL 

paper 

.25 
2.50 
.30 

.50 

.80 

.20 
.15 
2.OO 
.20 
.24 
5.OO 
.40 
.24 

l.oo 

.03 
pd. 
^ 
pd. 
.03 
pd. 
.05 
.03 
pd. 

»  Walsh's  Great  Rulers  of  the  World,  - 

- 

- 

Bas-Relief  s  of  12  Authors,  each. 

- 

- 

SINGING  AND  DIALOGUE  BOOKS. 

*Arbor  Day,  How  to  Celebrate  It,                            paper  .25  pd. 

Reception  Day  Series,  6  Nos.  (Set  $1.40  postpaid.)  Bach.    .30  .24  .03 

Song  Treasures.      -------     paper  .15  pd. 

*Rest  Primary  Songs,  new   -------  .15  pd. 

*Washington's  Birthday,  How  to  Celebrate  It,  -      paper  .25  pd, 

SCHOOL  AFFAEATUS. 

Smith's  Rapid  Practice  Arithmetic  Cards,  (32  sets),    Each,  .50     pd. 

"  Standard1"  Manikin.    (Sold  by  subscription.)    Price  on  application. 
"Man  Wonderful"  Manikin,       -      -       -      -  4.OO      pd. 

Standard  Blackboard  Stencils,  500  different  nos., 

from  5  to  50  cents  each.    Send  for  special  catalogue. 

"  Unique  "  Pencil  Sharpener,       -  1.50  .10 

*  Russell's  Solar  Lantern,    -----  25  OO     pd, 

Standard  Physician's  Manikin.  (Sold  by  subscription.) 

E^°"  100  page  classified,  illustrated,  descriptive  Catalogue  of  the  above 
and  many  other  Method  Books,  Teachers'  Helps,  sent  free.  100  page  Cat- 
logue'of  books  tor  teachers,  of  all|publishers,  light  school  apparatus,  etc., 
sent  free.  Each  of  these  contain  our  special  teachers'  prices. 

E.  L.  KELLOQQ  &  CO.,  New  York  &  Chicago. 


GENLKAL  METHODS  AND  SCHOOL  MANAGEMENT. 


J..UU 

1ft 

.uo 

*•       Art  of  Securing  Attention      -                    paper 

.*15 

pd. 

**       Lectures  on  Teaching,      -                                 cl.     1.25 

1.00 
.15 

pd! 

Hughes'  Mistakes  in  Teaching.  Best  edition.     -          cl.       .50 

.40 

J05 

*        Securing  and  Retaining  Attention,  Best  ed.  cl.       .50 

.40 

.05 

"        How  to  Keep  Order.       -                            paper 

.15 

pd. 

Keliogg's  School  Mimagement.    -                                cl.       .75 
McMurry's  How  to  Conduct  the  Recitation,      -      paper 
*  Parker's  Talks  on  Pedagogics.                                      cl.      1.50 

.60 
.15 
1.20 

.05 
pd. 
.12 

Talks  on  Teaching,         -                                cl.     1.25 

l.OO 
1.2O 

.09 
14 

*Page's  Theory  and  Practice  of  Teaching,        -         cl.       .80 
Patridge's  Qumcy  Methods,  illustrated,     -      -          cl.     1.75 
Quick's  How  to  Train  the  Memory,     -                    paper 

'.64 
1.4O 
.15 
.60 

'.08 
.13 
pd. 
08 

"iteinhart's  Principles  of  Education,         -                 cl,       ^25 

.20 

ios 

*         *•         Civics  in  Education,  -                                 cl.       .25 

.20 

.03 

*Rooper's  Object  Teaching,          -                                cl.       .25 

.20 

.03 

Sidgwic-k's  Stimulus  in  School,     -                            paper 
Shaw  and  Donneli's  School  Devices,    -                          cl.    1.25 
Southwick's  Quiz  Manual  of  Teaching,      -                 cL       .75 

.15 
1.00 
.60 

pd. 
UO 
.05 

Yonge's  Practical  Work  in  School,      -                    paper 

.15 

pd. 

METHODS  IN  SPECIAL  SUBJECTS. 

Augsburg's  Easy  Drawings  for  Geog.  Class,     -      paper     .50 
44          Easy  Things  to  Draw,       -       -      -     paper     .30 

.40 
.24 

.05 
.03 

*Burnz  Step  by  Step  Primer,        - 
Calkins'  How  to  Teach  Phonics,          -      -      -         cl.       .50 

.25 

.40 

Pdg 

Dewey's  How  to  Teach  Manners,        -                         cl.       .50 
Gladstone's  Object  Teaching,      -                             paper 

.40 
.15 
.15 

'.05 
pd. 
pd. 

*Iles'  A  Class  in  Geometry    -----                    .80 
Johnson's  Education  by  Doing,           -                         cl.       .50 

.24 
.40 

.03 
.05 

*Kellojrg's  How  to  Write  Compositions     -      -       paper 

15 

pd. 

Keilogg's  Geography  by  Map  Drawing      -                 cl.       .50 
*Picture  Language  Cards,  2  sets,  each, 
Seeley's  Grube  Method  of  Teaching  Arithmetic,        cl.      1.00 
Grube  Idea  in  Teaching  Arithmetic     -         cl.       .30 

.40 
.30 
.80 
.24 

.05 
pd. 

!03 

Smith's  Rapid  Practice  Cards,      -              -    32  sets,  each 

.50 

Woodhull's  Easy  Experiments  in  Science,         -          cl.       .50 

.40 

'.05 

PRIMARY  AND  KINDERGARTEN 

Calkins'  How  to  Teach  Phonics,          -                         cl.      .50 

.40 

.05 

Currie's  Early  Education,     -----           cl.     1.25 

1.00 

.08 

Gladstone's  Object  Teaching,      -                           paper 

.15 

pd. 

A  utobiography  of  Froebel,          —      •       -      -         cl.       .50 

.40 

.05 

Floffman  's  Kindergarten  Gifts,    -                             paper 

.15 

pd. 

Johnson's  Education  by  Doing,  -                                cl.       .50 

.40 

.05 

*Kilburn's  Manual  of  Elementary  Teaching    -                   1.50 

1.2O 

.10 

Parker's  Talks  on  Teaching,        -                                   cl.     1.25 

l.OO 

.09 

Patridge's  Quincy  Methods,         -                                cl.     1.75 

1.4O 

.13 

Uooper's  Object  Teaching,      -----      cl.       .25 
Seeley's  Grube  Method  of  Teaching  Arithmetic,         cl.     1.00 

.20 
.80 

.03 
J07 

Grube  Idea  in  Primary  Arithmetic,    -         cl.       .30 

.24 

.03 

'Sinclair's  First  Years  at  School,                :                cL      .75 

.60 

.06 

'    gg^'B  ALL  ofebgfeS  *6 

fc     B.  L.  KELLOGG  &  CO.,  NEW  YORK  &  CHICAGO. 

Aliens  Mind  Studies  for  Young  Teach- 

ERS.  By  JEROME  ALLEN,  Ph.D..  Associate  Editor  of  the 
SCHOOL  JOURNAL,  Prof,  of  Pedagogy,  Univ.  of  City  of 
N.  Y.  16mo,  large,  clear  type,  128  pp.  Cloth,  50  cents  ;  to 
teachers,  40  cents  ;  by  mailed  cents  extra. 

There  are  many  teachers  who 
Know  little  about  psychology, 
and  who  desire  to  be  better  in- 
formed concerning  its  princi- 
ples, especially  its  relation  to  the 
work  of  teaching.  For  the  aid 
of  such,  this  book  has  been  pre- 
pared. But  it  is  not  a  psj^chol- 
ogy—  only  an  introduction  to  it, 
aiming  to  give  some  funda- 
mental principles,  together  with 
something  concerning  the  phi- 
losophy of  education.  Its  meth- 
od is  subjective  rather  than  ob- 
jective, leading  the  student  to 
watch  mental  processes,  and 
draw  his  own  conclusions.  It 
is  written  in  language  easy  to 
be  comprehended,  and  has  many 
VEROME  ALLEN,  Ph.D.,  Associate  Editor  Practical  illustrations.  It  will 
of  the  Journal  and  Institute.  aid  the  teacher  in  his  daily  work 
in  dealing  with  mental  facts  and  states. 

To  most  teachers  psychology  seems  to  be  dry.  This  book  shows 
how  it  may  become  the  most  interesting  of  all  studies.  It  also 
shows  how  to  begin  the  knowledge  of  self.  "  We  cannot  know 
in  others  what  we  do  not  first  know  in  ourselves."  This  is  the 
key-note  of  this  book.  Students  of  elementary  psychology  will 
appreciate  this  feature  of  "  Mind  Studies." 
ITS  CONTENTS. 


CHAP. 

I.  How  to  Study  Mind. 
II.  Some  Facts  in  Mind  Growth. 

III.  Development. 

IV.  Mind  Incentives. 

V.  A  few  Fundamental  Principles 

Settled. 
VI.  Temperaments. 

VII.  Training  of  the  Senses. 

VIII.  Attention. 
IX.  Perception. 

X.  Abstraction. 

XI.  Faculties     used     in    Abstract 
Thinking. 


CHAP.  | 

XII.  From  the  Subjective  to  the, 
Conceptive. 

XIII.  The  Will. 

XIV.  Diseases  of  the  Will. 
XV.  Kinds  of  Memory. 

XVI.  The  Sensibilities. 
XVII.  Relation  of  the  Sensibilities 

to  the  Will. 

XVIII.  Training  of  the  Sensibilities. 
XIX.  Relation  of  the  Sensibilities 

to  Morality. 
XX.  The  Imagination. 
J     XXT    Imagination  in  its  Maturity. 
•  XXII.  Education  of  the  Moral  Seuae 


feklvb  ALL  ORDERS  tfo 

^.  L.  KELLOGG  &  CO.,  NEW  YORK  &  CHICAGO,    3 

Browning's  Educational  Theories. 

By  OSCAR  BROWNING,  M.A.,  of  King's  College,  Cambridge, 
Eng.  No.  8  of  Reading  Circle  Library  Series.  Cloth,  16mo, 
237  pp.  Price,  50  cents;  to  leacJiers,  40  cents;  by  mail,  5 
cents  extra. 

This  work  has  been  before  the  public  some  time,  and  for  a 
general  sketch  of  the  History  of  Education  it  has  no  superior. 
Our  edition  contains  several  new  features,  making  it  specially 
valuable  as  a  text-book  for  Normal  Schools,  Teachers'  Classes, 
Reading  Circles,  Teachers'  Institutes,  etc. ,  as  well  as  the  student 
of  education.  These  new  features  are:  (1)  Side-heads  giving  the 
subject  of  each  paragraph;  (2)  each  chapter  is  followed  by  an 
analysis;  (3)  a  very  full  new  index;  (4)  also  an  appendix  on 
"Froebel,"  and  the  "  American  Common  School." 

OUTLINE  OF   CONTENTS. 

I.  Education  among  the  Greeks — Music  and  Gymnastic  Theo- 
ries of  Plato  and  Aristotle;  II.  Roman  Education — Oratory;  III. 
Humanistic  Education;  IV.  The  Realists— Ratich  and  Comenius; 
V.  The  Naturalists  —  Rabelais  and  Montaigne;  VI.  English 
Humorists  and  Realists— Roger  Ascham  and  John  Milton;  VII. 
Locke;  VIII.  Jesuits  and  Jansenists;  IX.  Rousseau;  X.  Pes- 
talozzi;  XI.  Kant,  Fichte,  and  Herbart;  XII.  The  English  Pub- 
lic School ;  XIII.  Froebel ;  XIV.  The  American  Common 
School. 

PRESS  NOTICES. 

Ed.  Courant.— "  This  edition  surpasses  others  in  its  adaptability  to  gen- 
eral use." 

Col.  School  Journal.—"  Can  be  used  as  a  text-book  in  the  History  of 
Education." 

Pa.  Ed.  News.—"  A  volume  that  can  be  used  as  a  text-book  on  the  His- 
tory of  Education." 

School  Education,  Minn. — "  Beginning  with  the  Greeks,  the  author  pre- 
sents a  brief  hut  clear  outline  of  the  leading  educational  theories  down  to 
the  present  time." 

Ed.  Review.  Can.— "A  book  like  this,  introducing  the  teacher  to  the  great 
minds  that  have  worked  in  the  same  field,  cannot  but  be  a  powerful  stimulus 
to  him  in  his  work." 


BttNB  ALL  OKDMtS  TO 

E.  L.  KELLOGG  &  CO.,  NEW  YORK  &  CHICAGO,  tl 

Curries  Early  Education. 

"  The  Principles  and  Practice  of  Early  and  Infant  School 
Education."  By  JAMES  CURRIE,  A.  M.,  Prin.  Church  of 
Scotland  Training  College,  Edinburgh.  Author  of 
"  Common  School  Education,"  etc.  With  an  introduction 
by  Clarence  E.  Meleney,  A.  M.,  Supt.  Schools,  Paterson, 
N.  J.  Bound  in  blue  cloth,  gold,  16mo,  290  pp.  Price, 
$1.25  ;  to  teachers,  $1.00  ;  by  mail,  8  cents  extra. 

WHY    THIS    BOOK    IS    VALUABLE. 

1.  Pestalozzi  gave  New  England  its  educational  supremacy. 
The  Pestalozzian  wave  struck  this  country  more  than  forty 

vears  ago,  and  produced  a  mighty  shock.  It  set  New  Eng- 
land to  thinking.  Horace  Mann  became  eloquent  to  help  on 
the  change,  and  went  up  and  down  Massachusetts,  urging  in 
earnest  tones  the  change  proposed  by  the  Swiss  educator. 
What  gave  New  England  its  educational  supremacy  was  its 
reception  of  Pestalozzi's  doctrines.  Page,  Philbrick,  Barnard 
were  all  his  disciples. 

2.  It  is  the  work  of  one  of  the  best  expounders  of  Pes- 
talozzi. 

Forty  years  ago  there  was  an  upheaval  in  education.  Pes- 
talozzi's words  were  acting  like  yeast  upon  educators  ;  thou- 
sands had  been  to  visit  his  schools  at  Yverdun,  and  on  their 
return  to  their  own  lands  had  reported  the  wonderful  scenes 
they  had  witnessed.  Rev.  James  Currie  comprehended  the 
movement,  and  sought  to  introduce  it.  Grasping  the  ideas  of 
this  great  teacher,  he  spread  them  in  Scotland ;  but  that 
country  was  not  elastic  and  receptive.  Still,  Mr.  Currie's 
presentation  of  them  wrought  a  great  change,  and  he  is  to  be 
reckoned  as  the  most  powerful  exponent  of  the  new  ideas  in 
Scotland.  Hence  this  book,  which  contains  them,  must  be 
considered  as  a  treasure  by  the  educator. 

3.  This  volume  is  really  a  Manual  of  Principles  of  Teaching. 
It  exhibits  enough  of  the  principles  to  make  the  teacher 

intelligent  in  her  practice.  Most  manuals  give  details,  but  no 
foundation  principles.  The  first  part  lays  a  psychological 
basis-Miie  only  one  there  is  for  the  teacher  ;  and  this  is  done 
in  a  simple  and  concise  way.  He  declares  emphatically  that 
teaching  cannot  be  learned  empirically.  That  is,  that  one  can- 
not watch  a  teacher  and  see  how  he  does  it,  and  then,  imitat* 
ing,  claim  to  be  a  teacher.  The  principles  must  be  learned. 

4.  It  is  a  Manual  of  Practice  in  Teaching. 


nALL  ORDERS  TO 
0.,  NEW  YORK  &  CHICAGO.   53 


Standard  Ulack  ^Board  Stencils. 

AIDS  TO  ILLUSTRATION. 

The  need  of  illustration  in  the  work  of  the  school-room  is  felt  by  every 
teacher;  but  lack  of  skill  in  drawing  is  a  great  obstacle.  To  overcome  this 
we  are  manufacturing  an  entirely  new  line  of 
blackboard  stencils,  by  which  hundreds  of  ob- 
jects may  be  put  on  the  blackboard  quickly 
and  handsomely  by  any  teacher  however  inex- 
perienced in  drawing.  Indeed  it  can  be  done 
by  almost  any  pupil.  Our  blackboard  stencils 
beautify  the  school-room  and  make  it  attrac- 
tive. They  give  good  models  for  drawing  and 
writing  lessons.  They  assist  the  teacher  in 
illustrating  Geography,  Language,  Botany, 
and  History.  No  class-room  is  complete  with- 
out these  available  aids. 

Our  standard  blackboard  stencils  are  made 
of  tough  manilla  paper  of  grait  strength,  made 
specially  for  us,  on  which  the  design  is  traced. 
These  stencils  will  enable  the  teacher  to  put 
a  handsome  illustration  on  the  blackboard  in 
Language  Lessons,  Geography,  Physiology, 
History,  Botany,  etc.,  etc.,  and  thus  attract 
and  hold  the  attention  of  the  class.  These 
stencils  can  be  used  any  number  of  times. 
Five  to  ten  minutes  will  give  a  perfect  map,  or 
a  drawing  of  an  elephant,  children  playing,  etc.  A  large  and  perfect  map  of 
Europe,  24x30  inches,  showing  all  the  prominent  rivers,  Lakes,  mountains 
and  large  cities  can  be  made  in  eight  minutes.  Each  stencil  can  be  used  an 
indefinite  number  of  times,  and  only  requires  a  little  pulverized  chalk  for  im- 
mediate  use. 

WHY  THE  BEST. 

1.  All  our  designs  are  new  and  of  a  high  grade  of  artistic  merit. 

2.  The  nnimals.  plants,  children,  birds,  portraits, 
etc.,  etc.,  are  put  on  paper  17x2-2  inches  in  size.  The 
maps  are  usually  24x36  inches  in  size.  No  other 
stencils  on  the  market  compete  with  them  in  size. 

8.  The  maps  are  from  the  recent  surveys  and 
are  absolutely  correct  in  outline. 

4.  Each  figure  and  map  is  plainly  numbered  and 
named  to  correspond  with  the  catalogue. 

6.  Many  of  these  stencils  are  arranged  in  groups. 
Each  group  contains  fire  (5)  Stencils,  packed  in  a 
strong  envelope.  This  envelope  gives  us  a  secure 
way  of  sending  the  stencils  by  mail,  and  the  buyer 
a  neat  receptacle  to  pack  each  away  when  through 
using.  SOLD  IN  SINGLE:  NUMBERS  as  well  as  in 
groups. 

TWO  SAMPLES  FOR  TRIAL. 

A  simple  map  of  South  America  and  a  design 
suitable  for  a  language  or  drawing  lesson  will  be 
mailed  post  paid  for  10  cents.  We  will  also  send  a 
complete  catalogue. 


SEND  ALL  ORDERS  TO 

54  E.  L.  KELLOGG  &  CO.,  NEW  YORK  &  CHICAGO. 


MAPS. 

These  maps  are  made  on  special  ma- 
nilla  paper,  size  24x36  inches.  Price,  10 
cts.  each.  Please  order  by  number. 

501  Eastern  Hemisphere. 

502  Western  Hemisphere. 

503  Mercator's  Eastern  Hemisphere. 

504  Mercator's  Western  Hemisphere. 

505  North  America. 

506  South  America. 

507  Europe. 

508  Asia. 

509  Africa. 

510  Australia. 

511  British  Isles. 

512  Mexico. 

513  Canada. 

514  West  Indies. 

SEPARATE  STATES   AND   TERRITO- 
RIES. 

48  maps,  24x36  inches.  Price,  10  cents 
each,  as  follows :  Please  order  by  num- 
ber. 

524  Alaska.  548  Missouri. 

525  Alabama.  549  Minnesota. 

526  Arizona.  550  Montana. 

527  Arkansas.  551  N.  Hamp. 

528  California.  552  N.  Jersey. 

529  Colorado.  553  N.  Mexico. 

530  Conn.  554  New  York. 

531  Dakota.  555  Nebraska. 

532  Delaware.  556  Nevada. 

533  Florida.  557  N.  Carolina. 

534  Georgia.  S58  Ohio. 

535  Idaho.  559  Oregon. 

536  Illinois.  560  Penn. 

537  Indiana.  561  R.  Island. 

538  Ind.  Ter.  562  S.  Carolina. 

539  Iowa.  5fi3  Tenn. 

540  Kansas.  564  Texas. 

541  Kentucky.  565  Utah. 

542  Louisiana.  566  Vermont. 

543  Maine.  567  Virginia. 

544  Maryland.  568  Wash.  Ter. 

545  Mass.  569  West  Virginia. 

546  Michigan.  570  Wisconsin. 

547  Mississippi.          571  Wyoming. 

GROUPS  OF  STATES. 
Size  24x36  inches.    Please  order  by 
number. 

Price,  10  cents  each. 

515  NEW  ENGLAND,    comprising  Me., 
N.  H.,  Vt.,  Mass.,  R.  I.,  Ct. 

516  MIDDLE  ATLANTIC.— N.  Y.,  N.  J., 
Pa.,  Del.,  Md.,  Va.,  and  W.  Va. 

517  SOUTHERN  STATES  (three  groups). 
No.  I.-N.  C.,  S.  C.,  Ga.,  Fla.,  Ala.,  Miss., 
La.,  and  Tex. 

518  No.  II.-W.  Va.,  Va.,  N.  C.,  S.  C., 
Ga.,  Fla.,  Ala.,  and  Miss. 

519  No.  III.— Ark.,  La.,  Tex.,  and  In- 
dian Ter. 

520  CENTRAL  STATES  (two  groups).  No. 
I.— Minn.,  Wis.,   Mich.,   la.,   111.,   Ind., 
Ohio,  Mo.,  and  Ky. 

521  No.   II.— Dak.   Ter.,   Minn.,   Wis., 
Mich.,  Neb.,  la.,  111.,  Ind..  Ohio,  Kan., 
Mo.,  and  Ky. 


522  WESTERN    STATES    (two    groups). 
No.  L-Wash.    Ter.,   Idaho,  Mon.  Ter., 
Dak.  Ter.,  Oregon,  Wyoming  Ter.,  Neb., 
Cal.,  Nev.,  Utah,  Col.,  Kan.,   Arizona 
Ter.,  N.  Mex.,  Ind.  Ter.,  and  Tex. 

523  No.  Il.-Wash.    Ter.,   Idaho  Ter., 
Mon.  Ter.,  Oregon,  Wyoming  Ter.,  Cal., 
Nev.,  Utah  Ter.,  Col.,  Arizona  Ter.,  New 
Mex. 

LARGE  MAPS. 

These  stencils  make  maps  as  large  as 
the  largest  wall  maps. 

572  United  States,  34x56  inches.  Price, 
oO  cents. 

573  Mercator's  Eastern  and  Western 
Hemisphere  with  Western  Hemisphere 
repeated ,  34x56.    Price,  50  ce  n  ts. 

HISTORICAL   MAPS. 
Please  order  by  number. 

600  Mercator's  Eastern  and  Western 
Hemispheres  with  the  Western  Hemis- 
phere repeated,  showing  all  the  routes 
of  the  early  voyagers  to  America  ami 
around  the  world.    Price,  50  cents. 

601  Large  map  of  the  U.  S.  showing 
territorial  growth.    Price,  25  cents. 

FRENCH  AND  INDIAN  WAR. 
Five  maps,  each  24x36  in.    Price,  10 
cents  each.    Set,  50  cents. 

602  Map  of  Va.  and  Pa.,  showing  Wash- 
ington's home,  route  taken  in  his  jour- 
ney to  St.  Pierre,  Ft.  Duquesne. 

603  Map  of  N.  Y.,  showing  all  forts  on 
the  great  lakes  and  L;ike  Champlain. 

604  Canada,  showing  all  the  principal 
places  and  Nova  Scotia. 

605  Map  showing  British  possessions 
before  the  War. 

606  Map  showing  British  possessions 
after  the  War. 

WAR  OF    THE   REVOLUTfON.     ' 
Five  maps,  each  24x36  in.    Price,  50 
cents  each.    50  cents  a  set. 

607  Boston  and  vicinity.    N.  Y.  and 
vicinity. 

60S  Phila.,     Trenton,    Valley    Forge, 
Monmouth. 

609  Burgoyne's  Invasion. 

610  Yorktown   and    Southern   Battle 
Fields. 

611  Map  showing  Territory  of  U.  S.  at 
close  of  the  War. 

WAR  OF  1812. 

Three  maps,  size  24x36  in.  each.  Price, 
10  cents  each. 

612  Great  Lakes  and  vicinity,  showing 
battle  fields. 

613  Washington  and  vicinity. 

614  New  Orleans. 

CIVIL  WAR. 

Size,  24x36  in.    Price,  10  cents  each 
$1.00  a  set. 

615  U.  S.,  showing  territory  seceded. 

616  Washington  and  vicinity. 

617  Richmond  and  vicinity. 

618  Charleston  Harbor. 

619  Miss.  River,  New  Orleans,  etc 

620  Gettysburg  Campaign. 


SEND  ALL  ORDERS  TO 

E.  L.  KELLOGG  &  CO..  NEW  YORK  &  CHICAGO.    55 


621  Sherman's  March. 
622  Battle  Fields  of  Ky.  and  Tenn. 

Group  Fourteen—  ANIMALS. 
66  Wolf.                      69  Kangaroo. 

623  Battle  Field  of  Va. 

67  Fox.                       70  Donkey. 

624  Petersburg  and  Appoto  .  ax. 

C3  Hyena. 

MISCELLANEOUS. 

Group  Fifteen—  FLOWERS. 

Size,  17x:&   inches      Price,   singly,  5 

1  Wild  Rose.            74  Laurel  Spray. 
2  Calla  Lily.             75  Pear  Blossom. 

design,  25  cents. 

3  Solomon's  Seal. 

Group  One—  CHILDREN 
.  In  a  Swing.            4  Kite  Flying. 
2  Jumping  Rope.      5  Skating. 

Group  Sixteen—  FLOWERS. 
-6  Wood  Violet,        79  Morning  Glories. 
7  Pond  Lilies.          80  Fuchsias. 

3  Leap  Frog. 

8  Roses. 

Group  Two—  CHILDREN. 
6  Feeding  Doves.      9  On  a  Toboggan. 
7  RollingtheHoop.10  Where  am  I  ? 

Group  Seventeen—  BIRDS. 
81  Quails.                    84  Stork. 
S2  Woodcocks.          85  Swan. 

8  Blowing       Soap 
Bubbles. 

83  Eagle  Flying. 

Group  Three—  CHILDREN. 
11  Two  Lillfes.          14  Fast  Friends. 

Group  Eighteen—  OLD  AND  YOUNG. 
86  Hen  and  Chick-  88  Dut-k  and  Duck- 

12  Training  Pussy.  15  Dance,         Little 

ens,                             lings. 

13  What  Do  I  Care.          Baby. 
Group  Four-CHILDREN. 
16  Oh,  How  High  !    18  "  My  Pony  Loves 
17  Naughty        Tab          Sugar." 
and  Dash.          19  Can  I  Get  Them? 

87  Goose  and  Gos-  89  Owl  and  Owlets, 
lings.                   90  Bird  and  Young. 
Group  Nineteen—  BUILDINGS. 
91  Lighthouse.          94  Bird  House. 
93  Castle.                   95  Fort. 

:.'•>  Mud  Pies. 

!>3  Wind  Mill. 

Group  Five-CHILDREN. 
21  Saved          From  2S  Learning          to 
Drowning.                 Read. 
22  St.  Bernard  Dog  24  Who  Broke  the 
and  Boy                    Window  ? 

Group  Twenty-PATRIOTIC  LIST. 
'.Hi  The      American  99  The     American 

97  Llh't'-rty  IM1.          100  Goddess  of  Lib- 

25  The  Milkmaid. 

IB  U.    s.    Coat    of         erty. 

Group  SIX-CHILDREN. 

Arms. 

26  Wide  Awake.       29  The  Pet  Squirrel. 

BORDERS. 

27  Fast  Asleep.         30  Learning          to 

101  Spiral  Curves. 

28  Have  You  Been         Walk. 

102  Greek  Fret. 

Bathing  ? 

103  Triangular  Combinations. 

Group  Seveii-ON  THE  SEA-SHORE. 

104  Greek  Fret. 

81  Star  Fish.              84  Jelly  Fish. 
82  Hermit  Crab.       35  Red  Coral. 
83  Lobster. 

105  Greek  Pattern  Anthlmion. 
106  Egyptian  Lotos. 
107  Ivy  Leaf. 

Group  Eight-PRESIDENTS. 
86  Washington.        89  Lincoln. 

108  Dog  Wood. 
109  Holly  Leaf  and  Berries. 

87  Jefferson.             40  Grant. 

110  Holly  Leaf  and  Berries. 

88  Jackson. 
Group  Nine—  POETS. 
41  Whittier.               44  Bryant. 
42  Longfellow.         45  Tennyson. 

ROLLS  OF  HONOR. 
Ill  Script  Letters,  plain. 
112  Script  Letters,  fancy. 
113  Old  English  Letters. 

^^roupTen-DOMESTIC  ANIMALS. 
46  Cow  and  Calf.      49  Camel. 
47  Horse  and  Colt.  50  Reindeer. 
48  Elephant       and 
Baby 

114  German  Text. 
115  American  Eagle  on  Shield. 
116  Excelsior. 
WRITING  CHARTS. 
117  Capitals  and  Small  Letters. 

Group  Eleven-  DOMESTIC  ANIMALS. 
51  Dog.                         54  Pig. 
52  Cat.                        55  Goat. 

The  letters  are  nearly  6  in.  high.   Size 
of  Stencils  9x36  in.    The  set  contains  11 
charts.    Price,  50  cents  a  set. 

PHYSIOLOGY  CHARTS. 

Group  'Twelve—  SMALL  ANIMALS. 

Six  charts,  size  24x36  in.  each.    Price, 

56  Rabbit.                 59  Mouse. 

10  cents  each.    Set  50  cents. 

57  Bat.                        60  Lynx. 

118  Bones.               121  Lungs. 

58  Rat. 

119  Skull.                123  Liver. 

Group  Thirteen—  LARGE  WILD   ANI 

120  Heart.               124  Intestines. 

MALS. 
61  Polar  Bear.          64  Rhinoceros. 
62  Lion.                     65  Hippopotamus. 
63  Lioness. 

NATURAL  HISTORY  CHARTS. 
Price  each,  10  cents,  except  No.  12u 
Size  2-1x36  inches.  8  nos. 

And  many  others.    Full  catalogue  on  application. 


SEND  ALL  ORDERS  TO 

20    E.  L.  KELLOGG  &  CO.,  NEW  YORK  &  CHICAGO. 

Hughes  Securing  and  Retaining  Atten- 

TTON.  By  JAMES  L.  HUGHES,  Inspector  Schools,  Toronto, 
Canada,  author  of  "Mistakes  in  Teaching."  Cloth,  116  pp. 
Price,  50  cents;  to  teachers,  40  cents;  by  mail,  5  cents  extra. 

This  valuable  little  book  has  already  become  widely  known  to 
American  teachers.  Our  new  edition  has  been  almost  entirety 
re-written,  and  several  new  important  chapters  added.  It  is  the 
only  AUTHORIZED  COPYRIGHT  EDITION.  Caution. — Buy  no  other, 

WHAT   IT   CONTAINS. 

I.  General  Principles;  II.  Kinds  of  Attention;  III.  Characteristics  of  Good 
Attention;  IV.  Conditions  of  Attention;  V.  Essential  Characteristics  of  the 
Teacher  in  Securing  and  Retaining  Attention;  VI.  How  to  Control  a  Class; 
VII.  Methods  of  Stimulating  and  Controlling  a  Desire  for  Knowledge;  VIII. 
How  to  Gratify  and  Develop  the  Desire  for  Mental  Activity;  IX.  Distracting 
Attention;  X.  Training  the  Power  of  Attention;  XT.  General  Suggestions 
regarding  Attention. 

TESTIMONIALS. 

S.  P.  Bobbins,  Pres.  McGill  Normal  School.  Montreal,  Can.,  writes  to  Mr. 
Hughes:—"  It  is  quite  superfluous  for  me  to  say  that  your  little  books  are 
admirable.  I  was  yesterday  authorized  to  put  the  *  Attention '  on  the  list 
of  books  to  be  used  in  the  Normal  School  next  year.  Crisp  and  attractive 
in  style,  and  mighty  by  reason  of  its  good,  sound  common-sense,  it  is  a 
book  that  every  teacher  should  know." 

Popular  Educator  (Boston):—"  Mr.  Hughes  has  embodied  the  best  think- 
ing of  his  life  in  these  pages." 

Central  School  Journal  (la.).—"  Though  published  four  or  five  years 
since,  this  book  has  steadily  advanced  in  popularity." 

Educational  Courant  (Ky.).— "It  is  intensely  practical.  There  isn't  a 
mystical,  muddy  expression  in  the  book." 

Educational  Times  (England).—"  On  an  important  subject,  and  admir* 
ably  executed." 

School  Guardian  (England).—"  We  unhesitatingly  recommend  it." 

New  England  Journal  of  Education.—"  The  book  is  a  guide  and  a 
manual  of  special  value." 

New  York  School  Journal,—"  Every  teacher  would  derive  benefit  from 
reading  this  volume." 

Chicago  Educational  Weekly.— "  The  teacher  who  aims  at  best  sue- 

c_ss  should  study  it." 
Phii.  Teacher.—"  Many  who  have  spent  months  in  the  school-room  would 

be  benefited  by  it." 

Maryland  School  Journal.—"  Always  clear,  never  tedious;" 
Va.  Ed.  Journal. — "  Excellent  hints  as  to  securing  attention." 
Ohio  Educational  Monthly.—"  We  advise  readers  to  send  for  a  copy." 
""icific  Home  and  School  Journal.—"  An  excellent  little  manual." 


YB  04999 


/.fr 
A/7- 


WHVERSnY  OF  CALIFORNIA  LIBRARY 


